Multiperiod mean absolute deviation uncertain portfolio selection with real constraints

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. Most of existing mean–absolute deviation models are devoted to stochastic single-period portfolio optimization. However, practical investment decision problems often involve the uncerta...

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Vydáno v:Soft computing (Berlin, Germany) Ročník 23; číslo 13; s. 5081 - 5098
Hlavní autor: Zhang, Peng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2019
Springer Nature B.V
Témata:
Algorithms
Artificial Intelligence
Bankruptcy
Computational Intelligence
Control
Deviation
Dynamic programming
Engineering
Expected values
Fuzzy sets
Integers
Investment strategy
Iterative methods
Linear programming
Mathematical Logic and Foundations
Mechatronics
Methodologies and Application
Optimization
Random variables
Risk management
Robotics
Set theory
Stock exchanges
Uncertain modeling
Mean absolute deviation model
The discrete iteration method
Multiperiod portfolio optimization
Uncertainty theory
ISSN:1432-7643, 1433-7479
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Shrnutí:Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. Most of existing mean–absolute deviation models are devoted to stochastic single-period portfolio optimization. However, practical investment decision problems often involve the uncertain dynamic information. Considering transaction costs, borrowing constraints, threshold constraints, cardinality constraints and risk control, we present a novel multiperiod mean absolute deviation uncertain portfolio selection model, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. In proposed model, the return rate of asset and the risk are quantified by uncertain expected value and uncertain absolute deviation, respectively. Cardinality constraints limit the number of risky assets in the optimal portfolio. Threshold constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. Based on uncertainty theories, the model is transformed into a crisp dynamic optimization problem. Because of the transaction costs and cardinality constraints, the multiperiod portfolio selection is a mix integer dynamic optimization problem with path dependence, which is “NP hard” problem that is very difficult to solve. The proposed model is approximated to a mix integer dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-018-3176-z