Uncertain utility portfolio optimization based on two different criteria and improved whale optimization algorithm
Since Markowitz introduced the mean–variance model, many investors have described investment return rates by assuming they are stochastic or fuzzy variables. However, the inherent complexity and unpredictability of financial markets often render these assumptions insufficient. To address these chall...
Saved in:
| Published in: | Expert systems with applications Vol. 268; p. 126281 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Ltd
05.04.2025
|
| Subjects: | |
| ISSN: | 0957-4174 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Since Markowitz introduced the mean–variance model, many investors have described investment return rates by assuming they are stochastic or fuzzy variables. However, the inherent complexity and unpredictability of financial markets often render these assumptions insufficient. To address these challenges, an increasing number of researchers are exploring portfolio optimization within the framework of uncertainty theory. This paper proposes two portfolio optimization models that incorporate investors’ utility under the criteria of expected value and optimistic value. We derive the deterministic forms of these two models under the assumption that the variables follow uncertain normal distributions. Additionally, we compare the differences between the multi-factor expected value-standard deviation utility (ESU) model and the optimistic value-standard deviation utility (OSU) model in terms of their ability to maximize investors’ utility. To solve these models effectively, we propose an improved whale optimization algorithm (IWOA) based on the Levy flight strategy, adaptive position weight strategy, and adaptive probability threshold. Extensive numerical experiments validate the effectiveness of the improved algorithm and compare the differences between the two models. |
|---|---|
| AbstractList | Since Markowitz introduced the mean–variance model, many investors have described investment return rates by assuming they are stochastic or fuzzy variables. However, the inherent complexity and unpredictability of financial markets often render these assumptions insufficient. To address these challenges, an increasing number of researchers are exploring portfolio optimization within the framework of uncertainty theory. This paper proposes two portfolio optimization models that incorporate investors’ utility under the criteria of expected value and optimistic value. We derive the deterministic forms of these two models under the assumption that the variables follow uncertain normal distributions. Additionally, we compare the differences between the multi-factor expected value-standard deviation utility (ESU) model and the optimistic value-standard deviation utility (OSU) model in terms of their ability to maximize investors’ utility. To solve these models effectively, we propose an improved whale optimization algorithm (IWOA) based on the Levy flight strategy, adaptive position weight strategy, and adaptive probability threshold. Extensive numerical experiments validate the effectiveness of the improved algorithm and compare the differences between the two models. |
| ArticleNumber | 126281 |
| Author | Li, Bo Xu, Jiajun |
| Author_xml | – sequence: 1 givenname: Jiajun orcidid: 0009-0006-1742-9921 surname: Xu fullname: Xu, Jiajun email: xjj1044845675@163.com organization: School of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China – sequence: 2 givenname: Bo orcidid: 0000-0002-7796-9261 surname: Li fullname: Li, Bo email: libnust@163.com organization: School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China |
| BookMark | eNp9kMtOwzAQRb0oEm3hB1j5BxLsJM1DYoMqXlIlNnRtje0JnSqJK9u0Kl9PStnAgtXM4p4r3TNjk8ENyNiNFKkUsrzdphgOkGYiK1KZlVktJ2wqmkWVFLIqLtkshK0QshKimjK_Hgz6CDTwj0gdxSPfOR9b15Hjbhepp0-I5AauIaDl4xMPjltqW_Q4RG48RfQEHAbLqd95tx9jhw10-JuH7t2N2U1_xS5a6AJe_9w5Wz8-vC2fk9Xr08vyfpWYPKtjUlSFkbIWYEot6kIsmgbbyjZCZjo3eWVLK3OjSyh0DXIhdY4gRGkbA7rVxuZzlp17jXcheGzVzlMP_qikUCdTaqtOptTJlDqbGqH6D2Qofg-IHqj7H707oziO2hN6FQzhqNeSRxOVdfQf_gW9IIy7 |
| CitedBy_id | crossref_primary_10_12677_orf_2025_154221 |
| Cites_doi | 10.1016/j.asoc.2021.107854 10.1007/s10479-023-05524-x 10.1007/s10700-019-09308-6 10.1007/s00500-023-08265-y 10.1007/s10462-021-10114-z 10.1007/s00500-020-05423-4 10.1111/j.1465-7295.1997.tb01963.x 10.1016/j.frl.2023.104552 10.1016/j.knosys.2021.107625 10.1016/j.eswa.2018.08.027 10.1142/S0218488514500056 10.1007/s40747-020-00138-3 10.1016/j.eswa.2023.122059 10.1007/s10700-024-09433-x 10.1016/j.asoc.2021.107519 10.1016/j.chaos.2023.113198 10.1109/TCYB.2019.2925015 10.1007/s40815-022-01294-z 10.1111/mafi.12394 10.3233/JIFS-201769 10.1016/j.automatica.2022.110751 10.1016/S0377-2217(00)00298-8 10.1007/s10700-020-09345-6 10.1016/j.omega.2023.102943 10.1137/21M1450343 10.1016/j.ejor.2023.02.014 10.1287/mnsc.2021.4155 10.1109/TFUZZ.2018.2829463 10.1016/j.cam.2024.115859 10.1016/j.amc.2023.128301 10.1016/j.eswa.2024.124765 10.1103/PhysRevLett.73.2946 10.1016/j.automatica.2015.03.009 10.1016/j.advengsoft.2016.01.008 10.1016/j.sysconle.2023.105545 10.1016/j.asoc.2021.108104 10.1016/j.ins.2022.09.032 10.1016/j.ejor.2008.07.011 10.1007/s00500-019-04517-y 10.1007/s00366-019-00917-8 10.1155/2020/8834162 10.1016/j.cam.2020.112892 10.1016/j.eswa.2022.118896 10.1016/j.neunet.2021.10.007 10.1016/j.asoc.2023.110033 10.1016/j.pacfin.2024.102365 10.1016/j.eswa.2021.116308 10.1016/j.knosys.2020.106619 10.1007/s11579-024-00366-y 10.1016/j.matcom.2022.10.023 10.1016/j.matcom.2024.05.013 10.1016/j.asoc.2021.108084 10.1016/j.amc.2015.12.018 10.1007/s11831-020-09448-8 10.1051/ro/2019071 |
| ContentType | Journal Article |
| Copyright | 2024 Elsevier Ltd |
| Copyright_xml | – notice: 2024 Elsevier Ltd |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.eswa.2024.126281 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| ExternalDocumentID | 10_1016_j_eswa_2024_126281 S0957417424031488 |
| GroupedDBID | --K --M .DC .~1 0R~ 13V 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AABNK AACTN AAEDT AAEDW AAIKJ AAKOC AALRI AAOAW AAQFI AARIN AAXKI AAXUO AAYFN ABBOA ABFNM ABJNI ABMAC ABMVD ABUCO ACDAQ ACGFS ACHRH ACNTT ACRLP ACZNC ADBBV ADEZE ADTZH AEBSH AECPX AEIPS AEKER AENEX AFJKZ AFKWA AFTJW AGHFR AGUBO AGUMN AGYEJ AHHHB AHJVU AHZHX AIALX AIEXJ AIKHN AITUG AJOXV AKRWK ALEQD ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ANKPU AOUOD APLSM AXJTR BJAXD BKOJK BLXMC BNSAS CS3 DU5 EBS EFJIC EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HAMUX IHE J1W JJJVA KOM MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 ROL RPZ SDF SDG SDP SDS SES SEW SPC SPCBC SSB SSD SSL SST SSV SSZ T5K TN5 ~G- 29G 9DU AAAKG AAQXK AATTM AAYWO AAYXX ABKBG ABUFD ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADJOM ADMUD ADNMO AEUPX AFPUW AGQPQ AIGII AIIUN AKBMS AKYEP APXCP ASPBG AVWKF AZFZN CITATION EFKBS EFLBG EJD FEDTE FGOYB G-2 HLZ HVGLF HZ~ LG9 LY1 LY7 M41 R2- SBC SET WUQ XPP ZMT ~HD |
| ID | FETCH-LOGICAL-c328t-474c1180ac6b0840599ef7d9012b3c37d6d13cb6a4b8a151b3ea006d9cabfbcd3 |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001397334700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0957-4174 |
| IngestDate | Tue Nov 18 21:47:17 EST 2025 Sat Nov 29 03:07:48 EST 2025 Sat Feb 15 15:52:42 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Portfolio optimization Improved whale optimization algorithm Investors’ utility Optimistic value Uncertainty theory |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c328t-474c1180ac6b0840599ef7d9012b3c37d6d13cb6a4b8a151b3ea006d9cabfbcd3 |
| ORCID | 0000-0002-7796-9261 0009-0006-1742-9921 |
| ParticipantIDs | crossref_primary_10_1016_j_eswa_2024_126281 crossref_citationtrail_10_1016_j_eswa_2024_126281 elsevier_sciencedirect_doi_10_1016_j_eswa_2024_126281 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-04-05 |
| PublicationDateYYYYMMDD | 2025-04-05 |
| PublicationDate_xml | – month: 04 year: 2025 text: 2025-04-05 day: 05 |
| PublicationDecade | 2020 |
| PublicationTitle | Expert systems with applications |
| PublicationYear | 2025 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Markowitz (b36) 1952; 7 Dai, Qin (b11) 2021; 109 Huang, Meng, Xu (b21) 2024; 23 Chen, Li (b6) 2024; 446 Li, Shu, Sun, Teo (b27) 2021; 25 Yao, Ji (b54) 2014; 22 Sun, Wang, Chen, Liu (b46) 2018; 114 Lv, Zhang, Li (b34) 2024; 225 Kaidi, Khishe, Mohammadi (b22) 2022; 235 Chakraborty, Sharma, Saha, Saha (b4) 2022; 55 Lassance, Vrins (b23) 2023; 310 Mi, Xu (b37) 2023; 110 Huang, Jiang (b20) 2021; 20 Liu, Wang, Yuan, Zeng, Hone, Liu (b33) 2019; 51 Zhang, Li (b57) 2023; 177 Xu, Li (b51) 2024; 238 Chen, Li, Liu (b7) 2018; 27 Chen, Song, Shao, Wang, He, Chen (b8) 2024; 460 Abdel-Basset, Mohamed, Mirjalili (b1) 2021; 212 Yang, Chen, Liu, Zhang (b52) 2022; 24 Chang, Sun, Zhang, Peng (b5) 2020; 377 Fan, Chen, Li, Xia, Yu, Wang (b14) 2021; 37 Mirjalili, Lewis (b38) 2016; 95 Wang, Wang, Li, Li, Watada (b49) 2023; 134 Liu, Cao, Li (b32) 2021; 7 Wang, Ouyang, Li, Liu, Teng, Wang (b48) 2023; 58 Liu (b30) 2007 Shu, Li (b42) 2022; 60 Cuomo, Gatta, Giampaolo, Iorio, Piccialli (b10) 2022; 192 Desmettre, Steffensen (b13) 2023; 33 Zhang, Zhang, Xiao (b59) 2009; 197 Leung, Wang (b24) 2022; 145 Wu, Xie, Ge, Simone (b50) 2024; 332 Yang, Huang, Hong (b53) 2023; 27 Thakkar, Chaudhari (b47) 2021; 28 Li, Jiang, Guo, Ching, Yu (b26) 2020; 19 Saha (b40) 1997; 35 Zhai, Ye, Huang, Feng, Li (b55) 2020; 1 Deng, Liu, Fang, Qu, Huang (b12) 2023; 205 Huang, Di (b19) 2016; 276 Li, Huang (b25) 2023; 168 Gong, Min, Yu (b16) 2022; 114 Gupta (b18) 2022; 614 Li, Xu, Geng, Hong (b28) 2022; 114 Brito (b3) 2023; 213 Zhang, Yan, Wang, Wang (b58) 2024; 122 Gong, Xie, Zhou, Zhang (b17) 2024; 85 Shu, Pan, Ding, Zu (b43) 2024; 255 Cui, Bai, Ding, Parkes, Qu, He, Li (b9) 2020; 24 Steland (b44) 2024; 18 Parra, Terol, Uría (b39) 2001; 133 Fisher (b15) 1906 Sun, Chen (b45) 2021; 112 Shen (b41) 2015; 55 Zhou, Chen, Xiao, Ren, Jin (b60) 2019; 53 Liu (b31) 2010 Li, Zhang, Sun (b29) 2023; 147 Mantegna, Stanley (b35) 1994; 73 Blanchet, Chen, Zhou (b2) 2022; 68 Zhai, Zheng, Bai, Jiang (b56) 2021; 40 Cuomo (10.1016/j.eswa.2024.126281_b10) 2022; 192 Cui (10.1016/j.eswa.2024.126281_b9) 2020; 24 Kaidi (10.1016/j.eswa.2024.126281_b22) 2022; 235 Brito (10.1016/j.eswa.2024.126281_b3) 2023; 213 Li (10.1016/j.eswa.2024.126281_b29) 2023; 147 Shu (10.1016/j.eswa.2024.126281_b42) 2022; 60 Huang (10.1016/j.eswa.2024.126281_b19) 2016; 276 Yao (10.1016/j.eswa.2024.126281_b54) 2014; 22 Li (10.1016/j.eswa.2024.126281_b28) 2022; 114 Li (10.1016/j.eswa.2024.126281_b25) 2023; 168 Xu (10.1016/j.eswa.2024.126281_b51) 2024; 238 Desmettre (10.1016/j.eswa.2024.126281_b13) 2023; 33 Gong (10.1016/j.eswa.2024.126281_b17) 2024; 85 Sun (10.1016/j.eswa.2024.126281_b45) 2021; 112 Liu (10.1016/j.eswa.2024.126281_b30) 2007 Liu (10.1016/j.eswa.2024.126281_b31) 2010 Thakkar (10.1016/j.eswa.2024.126281_b47) 2021; 28 Abdel-Basset (10.1016/j.eswa.2024.126281_b1) 2021; 212 Chen (10.1016/j.eswa.2024.126281_b7) 2018; 27 Zhou (10.1016/j.eswa.2024.126281_b60) 2019; 53 Mi (10.1016/j.eswa.2024.126281_b37) 2023; 110 Saha (10.1016/j.eswa.2024.126281_b40) 1997; 35 Fisher (10.1016/j.eswa.2024.126281_b15) 1906 Dai (10.1016/j.eswa.2024.126281_b11) 2021; 109 Parra (10.1016/j.eswa.2024.126281_b39) 2001; 133 Chakraborty (10.1016/j.eswa.2024.126281_b4) 2022; 55 Chang (10.1016/j.eswa.2024.126281_b5) 2020; 377 Blanchet (10.1016/j.eswa.2024.126281_b2) 2022; 68 Yang (10.1016/j.eswa.2024.126281_b53) 2023; 27 Markowitz (10.1016/j.eswa.2024.126281_b36) 1952; 7 Mirjalili (10.1016/j.eswa.2024.126281_b38) 2016; 95 Sun (10.1016/j.eswa.2024.126281_b46) 2018; 114 Zhang (10.1016/j.eswa.2024.126281_b58) 2024; 122 Zhang (10.1016/j.eswa.2024.126281_b57) 2023; 177 Mantegna (10.1016/j.eswa.2024.126281_b35) 1994; 73 Shen (10.1016/j.eswa.2024.126281_b41) 2015; 55 Wu (10.1016/j.eswa.2024.126281_b50) 2024; 332 Zhai (10.1016/j.eswa.2024.126281_b55) 2020; 1 Chen (10.1016/j.eswa.2024.126281_b6) 2024; 446 Wang (10.1016/j.eswa.2024.126281_b49) 2023; 134 Gong (10.1016/j.eswa.2024.126281_b16) 2022; 114 Li (10.1016/j.eswa.2024.126281_b27) 2021; 25 Zhang (10.1016/j.eswa.2024.126281_b59) 2009; 197 Huang (10.1016/j.eswa.2024.126281_b21) 2024; 23 Leung (10.1016/j.eswa.2024.126281_b24) 2022; 145 Yang (10.1016/j.eswa.2024.126281_b52) 2022; 24 Wang (10.1016/j.eswa.2024.126281_b48) 2023; 58 Fan (10.1016/j.eswa.2024.126281_b14) 2021; 37 Huang (10.1016/j.eswa.2024.126281_b20) 2021; 20 Shu (10.1016/j.eswa.2024.126281_b43) 2024; 255 Liu (10.1016/j.eswa.2024.126281_b32) 2021; 7 Gupta (10.1016/j.eswa.2024.126281_b18) 2022; 614 Li (10.1016/j.eswa.2024.126281_b26) 2020; 19 Lv (10.1016/j.eswa.2024.126281_b34) 2024; 225 Deng (10.1016/j.eswa.2024.126281_b12) 2023; 205 Zhai (10.1016/j.eswa.2024.126281_b56) 2021; 40 Steland (10.1016/j.eswa.2024.126281_b44) 2024; 18 Chen (10.1016/j.eswa.2024.126281_b8) 2024; 460 Liu (10.1016/j.eswa.2024.126281_b33) 2019; 51 Lassance (10.1016/j.eswa.2024.126281_b23) 2023; 310 |
| References_xml | – volume: 51 start-page: 1085 year: 2019 end-page: 1093 ident: b33 article-title: A novel sigmoid-function-based adaptive weighted particle swarm optimizer publication-title: IEEE Transactions on Cybernetics – volume: 133 start-page: 287 year: 2001 end-page: 297 ident: b39 article-title: A fuzzy goal programming approach to portfolio selection publication-title: European Journal of Operational Research – volume: 95 start-page: 51 year: 2016 end-page: 67 ident: b38 article-title: The whale optimization algorithm publication-title: Advances in Engineering Software – volume: 7 start-page: 1711 year: 2021 end-page: 1722 ident: b32 article-title: Improving ant colony optimization algorithm with epsilon greedy and levy flight publication-title: Complex & Intelligent Systems – volume: 310 start-page: 302 year: 2023 end-page: 314 ident: b23 article-title: Portfolio selection: A target-distribution approach publication-title: European Journal of Operational Research – volume: 145 start-page: 68 year: 2022 end-page: 79 ident: b24 article-title: Cardinality-onstrained portfolio selection based on collaborative neurodynamic optimization publication-title: Neural Networks – volume: 114 year: 2022 ident: b16 article-title: Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels publication-title: Applied Soft Computing – year: 1906 ident: b15 article-title: The nature of capital and income – volume: 25 start-page: 3993 year: 2021 end-page: 4001 ident: b27 article-title: An optimistic value-variance-entropy model of uncertain portfolio optimization problem under different risk preferences publication-title: Soft Computing – year: 2010 ident: b31 article-title: Uncertainty theory: A branch of mathematics for modeling human uncertainty – volume: 192 year: 2022 ident: b10 article-title: An unsupervised learning framework for marketneutral portfolio publication-title: Expert Systems with Applications – volume: 68 start-page: 6382 year: 2022 end-page: 6410 ident: b2 article-title: Distributionally robust mean–variance portfolio selection with wasserstein distances publication-title: Management Science – volume: 20 start-page: 315 year: 2021 end-page: 330 ident: b20 article-title: Portfolio management with background risk under uncertain mean–variance utility publication-title: Fuzzy Optimization and Decision Making – volume: 23 start-page: 561 year: 2024 end-page: 575 ident: b21 article-title: Portfolio selection with second order uncertain dominance constraint publication-title: Fuzzy Optimization and Decision Making – volume: 168 year: 2023 ident: b25 article-title: Uncertain random portfolio selection with different mental accounts based on mixed data publication-title: Chaos, Solitons & Fractals – volume: 255 year: 2024 ident: b43 article-title: Resource scheduling optimization for industrial operating system using deep reinforcement learning and WOA algorithm publication-title: Expert Systems with Applications – volume: 35 start-page: 770 year: 1997 end-page: 782 ident: b40 article-title: Risk preference estimation in the nonlinear mean standard deviation approach publication-title: Economic Inquiry – volume: 24 start-page: 2798 year: 2022 end-page: 2812 ident: b52 article-title: A multi-period fuzzy portfolio optimization model with short selling constraints publication-title: International Journal of Fuzzy Systems – volume: 122 year: 2024 ident: b58 article-title: A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information publication-title: Omega – volume: 37 start-page: 1851 year: 2021 end-page: 1878 ident: b14 article-title: A new improved whale optimization algorithm with joint search mechanisms for high-dimensional global optimization problems publication-title: Engineering with Computers – volume: 18 start-page: 151 year: 2024 end-page: 170 ident: b44 article-title: Are minimum variance portfolios in multi-factor models long in low-beta assets? publication-title: Mathematics and Financial Economics – volume: 332 start-page: 617 year: 2024 end-page: 644 ident: b50 article-title: Nonconvex multi-period mean–variance portfolio optimization publication-title: Annals of Operations Research – year: 2007 ident: b30 article-title: Uncertainty theory – volume: 60 start-page: 2420 year: 2022 end-page: 2439 ident: b42 article-title: Stability and attractivity analysis of uncertain switched systems under optimistic value criterion publication-title: SIAM Journal on Control and Optimization – volume: 22 start-page: 113 year: 2014 end-page: 123 ident: b54 article-title: Uncertain decision making and its application to portfolio selection problem publication-title: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems – volume: 53 start-page: 1581 year: 2019 end-page: 1600 ident: b60 article-title: Performance evaluation of portfolios with fuzzy returns publication-title: RAIRO-Operations Research – volume: 73 start-page: 2946 year: 1994 end-page: 2949 ident: b35 article-title: Stochastic process with ultraslow convergence to a Gaussian: The truncated levy flight publication-title: Physical Review Letters – volume: 40 start-page: 5071 year: 2021 end-page: 5086 ident: b56 article-title: Multiperiod portfolio selection models under uncertain measure and with multiple criteria publication-title: Journal of Intelligent & Fuzzy Systems – volume: 1 start-page: 1 year: 2020 end-page: 19 ident: b55 article-title: Whale optimization algorithm for multiconstraint second-order stochastic dominance portfolio optimization publication-title: Computational Intelligence and Neuroscience – volume: 27 start-page: 11379 year: 2023 end-page: 11394 ident: b53 article-title: A new uncertain enhanced index tracking model with higher-order moment of the downside publication-title: Soft Computing – volume: 225 start-page: 216 year: 2024 end-page: 313 ident: b34 article-title: An uncertain bi-objective mean-entropy model for portfolio selection with realistic factors publication-title: Mathematics and Computers in Simulation – volume: 460 year: 2024 ident: b8 article-title: Optimistic value-based optimal control problems with uncertain discrete-time noncausal systems publication-title: Applied Mathematics and Computation – volume: 85 year: 2024 ident: b17 article-title: The enhanced benefits of ESG in portfolios: A multi-factor model perspective based on LightGBM publication-title: Pacific-Basin Finance Journal – volume: 110 start-page: 82 year: 2023 end-page: 105 ident: b37 article-title: Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory publication-title: Insurance: Mathematics & Economics – volume: 197 start-page: 693 year: 2009 end-page: 700 ident: b59 article-title: Portfolio selection under possibilistic mean–variance utility and a SMO algorithm publication-title: European Journal of Operational Research – volume: 212 year: 2021 ident: b1 article-title: A novel whale optimization algorithm integrated with Nelder–Mead simplex for multi-objective optimization problems publication-title: Knowledge-Based Systems – volume: 134 year: 2023 ident: b49 article-title: Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory publication-title: Applied Soft Computing – volume: 213 year: 2023 ident: b3 article-title: A portfolio stock selection model based on expected utility, entropy and variance publication-title: Expert Systems with Applications – volume: 147 year: 2023 ident: b29 article-title: Multi-period portfolio selection based on uncertainty theory with bankruptcy control and liquidity publication-title: Automatica – volume: 55 start-page: 165 year: 2015 end-page: 175 ident: b41 article-title: Mean–variance portfolio selection in a complete market with unbounded random coefficients publication-title: Automatica – volume: 114 year: 2022 ident: b28 article-title: A hybrid approach for forecasting ship motion using CNN-GRU-AM and GCWOA publication-title: Applied Soft Computing – volume: 109 year: 2021 ident: b11 article-title: Multi-period uncertain portfolio optimization model with minimum transaction lots and dynamic risk preference publication-title: Applied Soft Computing – volume: 55 start-page: 4605 year: 2022 end-page: 4716 ident: b4 article-title: A novel improved whale optimization algorithm to solve numerical optimization and real-world applications publication-title: Artificial Intelligence Review – volume: 112 year: 2021 ident: b45 article-title: Multi-population improved whale optimization algorithm for high dimensional optimization publication-title: Applied Soft Computing – volume: 205 start-page: 794 year: 2023 end-page: 817 ident: b12 article-title: A novel improved whale optimization algorithm for optimization problems with multi-strategy and hybrid algorithm publication-title: Mathematics and Computers in Simulation – volume: 19 start-page: 53 year: 2020 end-page: 79 ident: b26 article-title: On product of positive L-R fuzzy numbers and its application to multi-period portfolio selection problems publication-title: Fuzzy Optimization and Decision Making – volume: 7 start-page: 77 year: 1952 end-page: 91 ident: b36 article-title: Portfolio selection publication-title: The Journal of Finance – volume: 58 year: 2023 ident: b48 article-title: Multi-objective portfolio selection considering expected and total utility publication-title: Finance Research Letters – volume: 377 year: 2020 ident: b5 article-title: Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory publication-title: Journal of Computational and Applied Mathematics – volume: 238 year: 2024 ident: b51 article-title: Multiple-factor optimistic value based model and parameter estimation for uncertain portfolio optimization publication-title: Expert Systems with Applications – volume: 33 start-page: 946 year: 2023 end-page: 975 ident: b13 article-title: Equilibrium investment with random risk aversion publication-title: Mathematical Finance – volume: 177 year: 2023 ident: b57 article-title: Mean–variance portfolio selection under no-shorting rules: A BSDE approach publication-title: Systems & Control Letters – volume: 276 start-page: 284 year: 2016 end-page: 296 ident: b19 article-title: Uncertain portfolio selection with background risk publication-title: Applied Mathematics and Computation – volume: 446 year: 2024 ident: b6 article-title: An uncertainty theory based tri-objective behavioral portfolio selection model with loss aversion and reference level using a modified evolutionary root system growth algorithm publication-title: Journal of Computational and Applied Mathematics – volume: 235 year: 2022 ident: b22 article-title: Dynamic levy flight chimp optimization publication-title: Knowledge-Based Systems – volume: 27 start-page: 1023 year: 2018 end-page: 1036 ident: b7 article-title: A novel hybrid ICA-FA algorithm for multiperiod uncertain portfolio optimization model based on multiple criteria publication-title: IEEE Transactions on Fuzzy Systems – volume: 24 start-page: 2809 year: 2020 end-page: 2831 ident: b9 article-title: A hybrid combinatorial approach to a two-stage stochastic portfolio optimization model with uncertain asset prices publication-title: Soft Computing – volume: 114 start-page: 563 year: 2018 end-page: 577 ident: b46 article-title: A modified whale optimization algorithm for large-scale global optimization problems publication-title: Expert Systems with Applications – volume: 28 start-page: 2133 year: 2021 end-page: 2164 ident: b47 article-title: A comprehensive survey on portfolio optimization, stock price and trend prediction using particle swarm optimization publication-title: Archives of Computational Methods in Engineering – volume: 614 start-page: 240 year: 2022 end-page: 262 ident: b18 article-title: Portfolio optimization using elliptic entropy and semi-entropy of coherent fuzzy numbers publication-title: Information Sciences – volume: 112 year: 2021 ident: 10.1016/j.eswa.2024.126281_b45 article-title: Multi-population improved whale optimization algorithm for high dimensional optimization publication-title: Applied Soft Computing doi: 10.1016/j.asoc.2021.107854 – volume: 332 start-page: 617 issue: 1 year: 2024 ident: 10.1016/j.eswa.2024.126281_b50 article-title: Nonconvex multi-period mean–variance portfolio optimization publication-title: Annals of Operations Research doi: 10.1007/s10479-023-05524-x – volume: 19 start-page: 53 year: 2020 ident: 10.1016/j.eswa.2024.126281_b26 article-title: On product of positive L-R fuzzy numbers and its application to multi-period portfolio selection problems publication-title: Fuzzy Optimization and Decision Making doi: 10.1007/s10700-019-09308-6 – volume: 27 start-page: 11379 issue: 16 year: 2023 ident: 10.1016/j.eswa.2024.126281_b53 article-title: A new uncertain enhanced index tracking model with higher-order moment of the downside publication-title: Soft Computing doi: 10.1007/s00500-023-08265-y – year: 2007 ident: 10.1016/j.eswa.2024.126281_b30 – volume: 55 start-page: 4605 year: 2022 ident: 10.1016/j.eswa.2024.126281_b4 article-title: A novel improved whale optimization algorithm to solve numerical optimization and real-world applications publication-title: Artificial Intelligence Review doi: 10.1007/s10462-021-10114-z – volume: 25 start-page: 3993 issue: 5 year: 2021 ident: 10.1016/j.eswa.2024.126281_b27 article-title: An optimistic value-variance-entropy model of uncertain portfolio optimization problem under different risk preferences publication-title: Soft Computing doi: 10.1007/s00500-020-05423-4 – volume: 35 start-page: 770 issue: 4 year: 1997 ident: 10.1016/j.eswa.2024.126281_b40 article-title: Risk preference estimation in the nonlinear mean standard deviation approach publication-title: Economic Inquiry doi: 10.1111/j.1465-7295.1997.tb01963.x – volume: 58 year: 2023 ident: 10.1016/j.eswa.2024.126281_b48 article-title: Multi-objective portfolio selection considering expected and total utility publication-title: Finance Research Letters doi: 10.1016/j.frl.2023.104552 – volume: 235 year: 2022 ident: 10.1016/j.eswa.2024.126281_b22 article-title: Dynamic levy flight chimp optimization publication-title: Knowledge-Based Systems doi: 10.1016/j.knosys.2021.107625 – volume: 114 start-page: 563 year: 2018 ident: 10.1016/j.eswa.2024.126281_b46 article-title: A modified whale optimization algorithm for large-scale global optimization problems publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2018.08.027 – volume: 22 start-page: 113 issue: 01 year: 2014 ident: 10.1016/j.eswa.2024.126281_b54 article-title: Uncertain decision making and its application to portfolio selection problem publication-title: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems doi: 10.1142/S0218488514500056 – volume: 7 start-page: 1711 year: 2021 ident: 10.1016/j.eswa.2024.126281_b32 article-title: Improving ant colony optimization algorithm with epsilon greedy and levy flight publication-title: Complex & Intelligent Systems doi: 10.1007/s40747-020-00138-3 – volume: 238 year: 2024 ident: 10.1016/j.eswa.2024.126281_b51 article-title: Multiple-factor optimistic value based model and parameter estimation for uncertain portfolio optimization publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2023.122059 – volume: 23 start-page: 561 issue: 4 year: 2024 ident: 10.1016/j.eswa.2024.126281_b21 article-title: Portfolio selection with second order uncertain dominance constraint publication-title: Fuzzy Optimization and Decision Making doi: 10.1007/s10700-024-09433-x – volume: 109 year: 2021 ident: 10.1016/j.eswa.2024.126281_b11 article-title: Multi-period uncertain portfolio optimization model with minimum transaction lots and dynamic risk preference publication-title: Applied Soft Computing doi: 10.1016/j.asoc.2021.107519 – volume: 168 year: 2023 ident: 10.1016/j.eswa.2024.126281_b25 article-title: Uncertain random portfolio selection with different mental accounts based on mixed data publication-title: Chaos, Solitons & Fractals doi: 10.1016/j.chaos.2023.113198 – volume: 51 start-page: 1085 issue: 2 year: 2019 ident: 10.1016/j.eswa.2024.126281_b33 article-title: A novel sigmoid-function-based adaptive weighted particle swarm optimizer publication-title: IEEE Transactions on Cybernetics doi: 10.1109/TCYB.2019.2925015 – volume: 24 start-page: 2798 issue: 6 year: 2022 ident: 10.1016/j.eswa.2024.126281_b52 article-title: A multi-period fuzzy portfolio optimization model with short selling constraints publication-title: International Journal of Fuzzy Systems doi: 10.1007/s40815-022-01294-z – volume: 33 start-page: 946 issue: 3 year: 2023 ident: 10.1016/j.eswa.2024.126281_b13 article-title: Equilibrium investment with random risk aversion publication-title: Mathematical Finance doi: 10.1111/mafi.12394 – volume: 40 start-page: 5071 issue: 3 year: 2021 ident: 10.1016/j.eswa.2024.126281_b56 article-title: Multiperiod portfolio selection models under uncertain measure and with multiple criteria publication-title: Journal of Intelligent & Fuzzy Systems doi: 10.3233/JIFS-201769 – volume: 147 year: 2023 ident: 10.1016/j.eswa.2024.126281_b29 article-title: Multi-period portfolio selection based on uncertainty theory with bankruptcy control and liquidity publication-title: Automatica doi: 10.1016/j.automatica.2022.110751 – volume: 133 start-page: 287 issue: 2 year: 2001 ident: 10.1016/j.eswa.2024.126281_b39 article-title: A fuzzy goal programming approach to portfolio selection publication-title: European Journal of Operational Research doi: 10.1016/S0377-2217(00)00298-8 – volume: 20 start-page: 315 year: 2021 ident: 10.1016/j.eswa.2024.126281_b20 article-title: Portfolio management with background risk under uncertain mean–variance utility publication-title: Fuzzy Optimization and Decision Making doi: 10.1007/s10700-020-09345-6 – volume: 122 year: 2024 ident: 10.1016/j.eswa.2024.126281_b58 article-title: A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information publication-title: Omega doi: 10.1016/j.omega.2023.102943 – year: 2010 ident: 10.1016/j.eswa.2024.126281_b31 – volume: 60 start-page: 2420 issue: 4 year: 2022 ident: 10.1016/j.eswa.2024.126281_b42 article-title: Stability and attractivity analysis of uncertain switched systems under optimistic value criterion publication-title: SIAM Journal on Control and Optimization doi: 10.1137/21M1450343 – volume: 310 start-page: 302 issue: 1 year: 2023 ident: 10.1016/j.eswa.2024.126281_b23 article-title: Portfolio selection: A target-distribution approach publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2023.02.014 – volume: 68 start-page: 6382 issue: 9 year: 2022 ident: 10.1016/j.eswa.2024.126281_b2 article-title: Distributionally robust mean–variance portfolio selection with wasserstein distances publication-title: Management Science doi: 10.1287/mnsc.2021.4155 – volume: 27 start-page: 1023 issue: 5 year: 2018 ident: 10.1016/j.eswa.2024.126281_b7 article-title: A novel hybrid ICA-FA algorithm for multiperiod uncertain portfolio optimization model based on multiple criteria publication-title: IEEE Transactions on Fuzzy Systems doi: 10.1109/TFUZZ.2018.2829463 – volume: 446 year: 2024 ident: 10.1016/j.eswa.2024.126281_b6 article-title: An uncertainty theory based tri-objective behavioral portfolio selection model with loss aversion and reference level using a modified evolutionary root system growth algorithm publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2024.115859 – volume: 460 year: 2024 ident: 10.1016/j.eswa.2024.126281_b8 article-title: Optimistic value-based optimal control problems with uncertain discrete-time noncausal systems publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2023.128301 – volume: 255 year: 2024 ident: 10.1016/j.eswa.2024.126281_b43 article-title: Resource scheduling optimization for industrial operating system using deep reinforcement learning and WOA algorithm publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2024.124765 – volume: 73 start-page: 2946 issue: 22 year: 1994 ident: 10.1016/j.eswa.2024.126281_b35 article-title: Stochastic process with ultraslow convergence to a Gaussian: The truncated levy flight publication-title: Physical Review Letters doi: 10.1103/PhysRevLett.73.2946 – volume: 55 start-page: 165 year: 2015 ident: 10.1016/j.eswa.2024.126281_b41 article-title: Mean–variance portfolio selection in a complete market with unbounded random coefficients publication-title: Automatica doi: 10.1016/j.automatica.2015.03.009 – volume: 95 start-page: 51 year: 2016 ident: 10.1016/j.eswa.2024.126281_b38 article-title: The whale optimization algorithm publication-title: Advances in Engineering Software doi: 10.1016/j.advengsoft.2016.01.008 – volume: 177 year: 2023 ident: 10.1016/j.eswa.2024.126281_b57 article-title: Mean–variance portfolio selection under no-shorting rules: A BSDE approach publication-title: Systems & Control Letters doi: 10.1016/j.sysconle.2023.105545 – volume: 114 year: 2022 ident: 10.1016/j.eswa.2024.126281_b16 article-title: Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels publication-title: Applied Soft Computing doi: 10.1016/j.asoc.2021.108104 – volume: 7 start-page: 77 issue: 1 year: 1952 ident: 10.1016/j.eswa.2024.126281_b36 article-title: Portfolio selection publication-title: The Journal of Finance – volume: 614 start-page: 240 year: 2022 ident: 10.1016/j.eswa.2024.126281_b18 article-title: Portfolio optimization using elliptic entropy and semi-entropy of coherent fuzzy numbers publication-title: Information Sciences doi: 10.1016/j.ins.2022.09.032 – volume: 197 start-page: 693 issue: 2 year: 2009 ident: 10.1016/j.eswa.2024.126281_b59 article-title: Portfolio selection under possibilistic mean–variance utility and a SMO algorithm publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2008.07.011 – volume: 24 start-page: 2809 year: 2020 ident: 10.1016/j.eswa.2024.126281_b9 article-title: A hybrid combinatorial approach to a two-stage stochastic portfolio optimization model with uncertain asset prices publication-title: Soft Computing doi: 10.1007/s00500-019-04517-y – volume: 37 start-page: 1851 year: 2021 ident: 10.1016/j.eswa.2024.126281_b14 article-title: A new improved whale optimization algorithm with joint search mechanisms for high-dimensional global optimization problems publication-title: Engineering with Computers doi: 10.1007/s00366-019-00917-8 – year: 1906 ident: 10.1016/j.eswa.2024.126281_b15 – volume: 1 start-page: 1 year: 2020 ident: 10.1016/j.eswa.2024.126281_b55 article-title: Whale optimization algorithm for multiconstraint second-order stochastic dominance portfolio optimization publication-title: Computational Intelligence and Neuroscience doi: 10.1155/2020/8834162 – volume: 377 year: 2020 ident: 10.1016/j.eswa.2024.126281_b5 article-title: Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory publication-title: Journal of Computational and Applied Mathematics doi: 10.1016/j.cam.2020.112892 – volume: 213 year: 2023 ident: 10.1016/j.eswa.2024.126281_b3 article-title: A portfolio stock selection model based on expected utility, entropy and variance publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2022.118896 – volume: 145 start-page: 68 year: 2022 ident: 10.1016/j.eswa.2024.126281_b24 article-title: Cardinality-onstrained portfolio selection based on collaborative neurodynamic optimization publication-title: Neural Networks doi: 10.1016/j.neunet.2021.10.007 – volume: 134 year: 2023 ident: 10.1016/j.eswa.2024.126281_b49 article-title: Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory publication-title: Applied Soft Computing doi: 10.1016/j.asoc.2023.110033 – volume: 85 year: 2024 ident: 10.1016/j.eswa.2024.126281_b17 article-title: The enhanced benefits of ESG in portfolios: A multi-factor model perspective based on LightGBM publication-title: Pacific-Basin Finance Journal doi: 10.1016/j.pacfin.2024.102365 – volume: 192 year: 2022 ident: 10.1016/j.eswa.2024.126281_b10 article-title: An unsupervised learning framework for marketneutral portfolio publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2021.116308 – volume: 212 year: 2021 ident: 10.1016/j.eswa.2024.126281_b1 article-title: A novel whale optimization algorithm integrated with Nelder–Mead simplex for multi-objective optimization problems publication-title: Knowledge-Based Systems doi: 10.1016/j.knosys.2020.106619 – volume: 18 start-page: 151 issue: 1 year: 2024 ident: 10.1016/j.eswa.2024.126281_b44 article-title: Are minimum variance portfolios in multi-factor models long in low-beta assets? publication-title: Mathematics and Financial Economics doi: 10.1007/s11579-024-00366-y – volume: 205 start-page: 794 year: 2023 ident: 10.1016/j.eswa.2024.126281_b12 article-title: A novel improved whale optimization algorithm for optimization problems with multi-strategy and hybrid algorithm publication-title: Mathematics and Computers in Simulation doi: 10.1016/j.matcom.2022.10.023 – volume: 225 start-page: 216 year: 2024 ident: 10.1016/j.eswa.2024.126281_b34 article-title: An uncertain bi-objective mean-entropy model for portfolio selection with realistic factors publication-title: Mathematics and Computers in Simulation doi: 10.1016/j.matcom.2024.05.013 – volume: 114 year: 2022 ident: 10.1016/j.eswa.2024.126281_b28 article-title: A hybrid approach for forecasting ship motion using CNN-GRU-AM and GCWOA publication-title: Applied Soft Computing doi: 10.1016/j.asoc.2021.108084 – volume: 276 start-page: 284 year: 2016 ident: 10.1016/j.eswa.2024.126281_b19 article-title: Uncertain portfolio selection with background risk publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2015.12.018 – volume: 28 start-page: 2133 issue: 4 year: 2021 ident: 10.1016/j.eswa.2024.126281_b47 article-title: A comprehensive survey on portfolio optimization, stock price and trend prediction using particle swarm optimization publication-title: Archives of Computational Methods in Engineering doi: 10.1007/s11831-020-09448-8 – volume: 53 start-page: 1581 issue: 5 year: 2019 ident: 10.1016/j.eswa.2024.126281_b60 article-title: Performance evaluation of portfolios with fuzzy returns publication-title: RAIRO-Operations Research doi: 10.1051/ro/2019071 – volume: 110 start-page: 82 year: 2023 ident: 10.1016/j.eswa.2024.126281_b37 article-title: Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory publication-title: Insurance: Mathematics & Economics |
| SSID | ssj0017007 |
| Score | 2.465501 |
| Snippet | Since Markowitz introduced the mean–variance model, many investors have described investment return rates by assuming they are stochastic or fuzzy variables.... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 126281 |
| SubjectTerms | Improved whale optimization algorithm Investors’ utility Optimistic value Portfolio optimization Uncertainty theory |
| Title | Uncertain utility portfolio optimization based on two different criteria and improved whale optimization algorithm |
| URI | https://dx.doi.org/10.1016/j.eswa.2024.126281 |
| Volume | 268 |
| WOSCitedRecordID | wos001397334700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0957-4174 databaseCode: AIEXJ dateStart: 19950101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0017007 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Jb9QwFLaGlgMXdtSyyQduUaqJ49jJsaAi4FBxaKU5ETm2Q2c0Tapppu3P53mdTIGKHrhEUWI7kb_PLy9-G0IfmNZ53oosZYUoUqoYrDmVFalQstREsEqT1hab4MfH5WxWfZ9MfoRYmKsl77ry5qa6-K9QwzUA24TO3gPuOChcgHMAHY4AOxz_CfhTgNGa-RN4iFWyjYrd9st5n_QgIM595GViPmDKGguu-1goZUhAjJj8zcKZFeyeg3FRPxPGDXHcXyx_9tD27Hxrd9-kTh58gugQOjcykgeAZ2vLn7lYrDdOQdaz4GM_3okghXVgKba2FHlKM1d1J0hX4qrmePmYEUZciZbfRLfbRVgc6Mtrkw-K0INN4-082be-X9GrMDisLWozRm3GqN0YD9Au4UUFUm_38OvR7Fu0M_GpC6gPb-7DqpwH4O03-bPqMlJHTp6ix_4_Ah86_J-hie6eoyehRgf2IvsFWkU6YE8HHOmAx3BiSwcMJ0AHHOmAAx0w0AEHOmBLh-3-kQ4v0enno5NPX1JfZyOVOSmHlHIqTSZAIVkzhR9-mCjdcgWaImlymXPFVJbLhgnalAI0xCbXAoS1qqRo2kaq_BXa6fpO7yHcmvuwzjUnmlaKVmSqGYG5L7WqCir2URamsJY-Cb2phbKs_w7ePkpinwuXguXO1kVApvZKpFMOayDaHf1e3-spb9CjzQp4i3aG1Vq_Qw_l1TC_XL33LPsFKdmaIw |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Uncertain+utility+portfolio+optimization+based+on+two+different+criteria+and+improved+whale+optimization+algorithm&rft.jtitle=Expert+systems+with+applications&rft.au=Xu%2C+Jiajun&rft.au=Li%2C+Bo&rft.date=2025-04-05&rft.issn=0957-4174&rft.volume=268&rft.spage=126281&rft_id=info:doi/10.1016%2Fj.eswa.2024.126281&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_eswa_2024_126281 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0957-4174&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0957-4174&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0957-4174&client=summon |