A neurodynamic approach for solving portfolio optimisation problem in high-frequency trading based on charnes-chooper transformation

This study addresses real-time portfolio optimisation in high-frequency trading by formulating it as a single-ratio fractional programming problem. By utilising the Charnes-Cooper transformation, we convert fractional programming into non-fractional programming. Subsequently, we introduce a projecti...

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Published in:International journal of systems science Vol. 56; no. 7; pp. 1561 - 1576
Main Authors: Zhu, Wenli, Chen, Jia, Hu, Jin
Format: Journal Article
Language:English
Published: London Taylor & Francis 19.05.2025
Taylor & Francis Ltd
Subjects:
Charnes-Cooper transformation
Mathematical programming
Neural networks
neurodynamic optimisation
Optimization
Portfolio optimisation
Real time
Systems science
ISSN:0020-7721, 1464-5319
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Abstract This study addresses real-time portfolio optimisation in high-frequency trading by formulating it as a single-ratio fractional programming problem. By utilising the Charnes-Cooper transformation, we convert fractional programming into non-fractional programming. Subsequently, we introduce a projection neural network to solve this non-fractional programming efficiently. Theoretical analysis substantiates that our neural network model exhibits exponential convergence to the optimal solution of the problem, underpinning its efficacy. The numerical simulations validate the reliability and efficiency of the obtained results.
AbstractList This study addresses real-time portfolio optimisation in high-frequency trading by formulating it as a single-ratio fractional programming problem. By utilising the Charnes-Cooper transformation, we convert fractional programming into non-fractional programming. Subsequently, we introduce a projection neural network to solve this non-fractional programming efficiently. Theoretical analysis substantiates that our neural network model exhibits exponential convergence to the optimal solution of the problem, underpinning its efficacy. The numerical simulations validate the reliability and efficiency of the obtained results.
Author Chen, Jia
Zhu, Wenli
Hu, Jin
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  fullname: Chen, Jia
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  surname: Hu
  fullname: Hu, Jin
  email: jhu@cqjtu.edu.cn
  organization: Chongqing Jiaotong University
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10.1109/31.1783
10.1016/j.neunet.2011.09.001
10.1016/j.neunet.2021.10.007
10.1109/TSMCB.2011.2140395
10.1016/j.neunet.2004.05.006
10.1016/S0305-0548(99)00059-3
10.1016/j.eswa.2023.120934
10.1162/089976604322860730
10.1109/TNN.2006.879774
10.1137/S1052623499361233
10.3905/jpm.1994.409501
10.1016/j.neucom.2020.12.045
10.1287/opre.24.3.452
10.1007/s11432-020-2894-9
10.1109/TETCI.2024.3369667
10.1016/j.neucom.2020.04.023
10.1287/mnsc.22.8.858
10.1016/j.neunet.2022.06.023
10.1109/TSMCB.2012.2198812
10.1007/s11063-019-10086-w
10.1016/j.neunet.2022.03.011
10.1016/0893-6080(94)90041-8
10.1109/TNNLS.2023.3307192
10.1007/BF00935552
10.1002/nav.3800090303
10.1109/TNNLS.2023.3311169
10.1109/81.995659
10.1287/mnsc.30.10.1143
10.1109/TNN.2011.2169682
10.1016/j.cor.2009.12.003
10.2307/2975974
10.1109/TCS.1986.1085953
10.3390/biomimetics7030124
10.1109/TNNLS.2017.2652478
10.1007/978-3-642-45780-7_7
10.1215/S0012-7094-43-01059-2
10.1109/TCYB.2021.3088884
10.1109/TNNLS.2013.2244908
10.1016/j.eswa.2022.116631
10.1109/TNNLS.2016.2549566
10.1109/TSMC.2023.3288224
10.1109/82.160169
10.1111/j.1540-6261.1976.tb03217.x
10.1086/294846
10.1007/s10107990015a
10.1007/s10957-005-2669-y
10.1007/11759966_55
10.1007/BF02026600
10.1109/ISCAS.2011.5937759
10.1016/j.amc.2022.127700
10.1007/s10614-022-10303-0
10.1109/72.548188
10.1109/TNN.2004.824252
10.1109/TSMCB.2007.903706
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References e_1_3_3_52_1
e_1_3_3_50_1
e_1_3_3_18_1
e_1_3_3_39_1
e_1_3_3_14_1
e_1_3_3_37_1
e_1_3_3_16_1
e_1_3_3_35_1
e_1_3_3_10_1
e_1_3_3_33_1
e_1_3_3_56_1
e_1_3_3_12_1
e_1_3_3_31_1
e_1_3_3_54_1
Bellman R. (e_1_3_3_2_1) 1943; 10
e_1_3_3_40_1
e_1_3_3_7_1
e_1_3_3_9_1
e_1_3_3_29_1
Kinderlehrer D. (e_1_3_3_25_1) 1980
e_1_3_3_48_1
e_1_3_3_27_1
e_1_3_3_46_1
e_1_3_3_3_1
e_1_3_3_21_1
e_1_3_3_44_1
e_1_3_3_5_1
e_1_3_3_23_1
e_1_3_3_42_1
e_1_3_3_30_1
e_1_3_3_51_1
e_1_3_3_17_1
e_1_3_3_19_1
e_1_3_3_13_1
e_1_3_3_38_1
e_1_3_3_15_1
e_1_3_3_36_1
e_1_3_3_57_1
e_1_3_3_34_1
e_1_3_3_55_1
e_1_3_3_11_1
e_1_3_3_32_1
e_1_3_3_53_1
e_1_3_3_41_1
e_1_3_3_6_1
e_1_3_3_8_1
e_1_3_3_28_1
e_1_3_3_24_1
e_1_3_3_49_1
e_1_3_3_26_1
e_1_3_3_47_1
e_1_3_3_20_1
e_1_3_3_45_1
e_1_3_3_4_1
e_1_3_3_22_1
e_1_3_3_43_1
References_xml – ident: e_1_3_3_30_1
  doi: 10.1016/j.neunet.2013.11.007
– ident: e_1_3_3_20_1
  doi: 10.1109/31.1783
– ident: e_1_3_3_32_1
  doi: 10.1016/j.neunet.2011.09.001
– ident: e_1_3_3_26_1
  doi: 10.1016/j.neunet.2021.10.007
– ident: e_1_3_3_33_1
  doi: 10.1109/TSMCB.2011.2140395
– ident: e_1_3_3_50_1
  doi: 10.1016/j.neunet.2004.05.006
– ident: e_1_3_3_53_1
  doi: 10.1016/S0305-0548(99)00059-3
– ident: e_1_3_3_3_1
  doi: 10.1016/j.eswa.2023.120934
– ident: e_1_3_3_49_1
  doi: 10.1162/089976604322860730
– ident: e_1_3_3_15_1
  doi: 10.1109/TNN.2006.879774
– ident: e_1_3_3_42_1
  doi: 10.1137/S1052623499361233
– ident: e_1_3_3_44_1
  doi: 10.3905/jpm.1994.409501
– ident: e_1_3_3_29_1
  doi: 10.1016/j.neucom.2020.12.045
– ident: e_1_3_3_40_1
  doi: 10.1287/opre.24.3.452
– ident: e_1_3_3_23_1
  doi: 10.1007/s11432-020-2894-9
– ident: e_1_3_3_52_1
  doi: 10.1109/TETCI.2024.3369667
– ident: e_1_3_3_18_1
  doi: 10.1016/j.neucom.2020.04.023
– ident: e_1_3_3_41_1
  doi: 10.1287/mnsc.22.8.858
– ident: e_1_3_3_27_1
  doi: 10.1016/j.neunet.2022.06.023
– ident: e_1_3_3_31_1
  doi: 10.1109/TSMCB.2012.2198812
– ident: e_1_3_3_17_1
  doi: 10.1007/s11063-019-10086-w
– ident: e_1_3_3_57_1
  doi: 10.1016/j.neunet.2022.03.011
– ident: e_1_3_3_47_1
  doi: 10.1016/0893-6080(94)90041-8
– ident: e_1_3_3_5_1
  doi: 10.1109/TNNLS.2023.3307192
– ident: e_1_3_3_45_1
  doi: 10.1007/BF00935552
– ident: e_1_3_3_7_1
  doi: 10.1002/nav.3800090303
– ident: e_1_3_3_6_1
  doi: 10.1109/TNNLS.2023.3311169
– ident: e_1_3_3_51_1
  doi: 10.1109/81.995659
– ident: e_1_3_3_38_1
  doi: 10.1287/mnsc.30.10.1143
– ident: e_1_3_3_14_1
  doi: 10.1109/TNN.2011.2169682
– ident: e_1_3_3_9_1
  doi: 10.1016/j.cor.2009.12.003
– ident: e_1_3_3_37_1
  doi: 10.2307/2975974
– ident: e_1_3_3_46_1
  doi: 10.1109/TCS.1986.1085953
– ident: e_1_3_3_24_1
  doi: 10.3390/biomimetics7030124
– ident: e_1_3_3_55_1
  doi: 10.1109/TNNLS.2017.2652478
– ident: e_1_3_3_13_1
  doi: 10.1007/978-3-642-45780-7_7
– volume: 10
  start-page: 643
  year: 1943
  ident: e_1_3_3_2_1
  article-title: The stability of solutions of linear differential equations
  publication-title: Duke Mathematical Journal
  doi: 10.1215/S0012-7094-43-01059-2
– ident: e_1_3_3_28_1
  doi: 10.1109/TCYB.2021.3088884
– ident: e_1_3_3_35_1
  doi: 10.1109/TNNLS.2013.2244908
– ident: e_1_3_3_21_1
  doi: 10.1016/j.eswa.2022.116631
– ident: e_1_3_3_36_1
  doi: 10.1109/TNNLS.2016.2549566
– volume-title: An introduction to variational inequalities and their applications
  year: 1980
  ident: e_1_3_3_25_1
– ident: e_1_3_3_4_1
  doi: 10.1109/TSMC.2023.3288224
– ident: e_1_3_3_56_1
  doi: 10.1109/82.160169
– ident: e_1_3_3_10_1
  doi: 10.1111/j.1540-6261.1976.tb03217.x
– ident: e_1_3_3_43_1
  doi: 10.1086/294846
– ident: e_1_3_3_11_1
  doi: 10.1007/s10107990015a
– ident: e_1_3_3_8_1
  doi: 10.1007/s10957-005-2669-y
– ident: e_1_3_3_12_1
  doi: 10.1007/11759966_55
– ident: e_1_3_3_39_1
  doi: 10.1007/BF02026600
– ident: e_1_3_3_34_1
  doi: 10.1109/ISCAS.2011.5937759
– ident: e_1_3_3_19_1
  doi: 10.1016/j.amc.2022.127700
– ident: e_1_3_3_22_1
  doi: 10.1007/s10614-022-10303-0
– ident: e_1_3_3_48_1
  doi: 10.1109/72.548188
– ident: e_1_3_3_54_1
  doi: 10.1109/TNN.2004.824252
– ident: e_1_3_3_16_1
  doi: 10.1109/TSMCB.2007.903706
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SubjectTerms Charnes-Cooper transformation
Mathematical programming
Neural networks
neurodynamic optimisation
Optimization
Portfolio optimisation
Real time
Systems science
Title A neurodynamic approach for solving portfolio optimisation problem in high-frequency trading based on charnes-chooper transformation
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