Noncooperative Game Strategy in Cyber-Financial Systems With Wiener and Poisson Random Fluctuations: LMIs-Constrained MOEA Approach

The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope their investment policies to be with the not only high profit but also low risk. Managers and investors involved pursue their own interests whic...

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Vydáno v:IEEE transactions on cybernetics Ročník 48; číslo 12; s. 3323 - 3336
Hlavní autoři: Chen, Bor-Sen, Chen, Wei-Yu, Yang , Chun-Tao, Yan, Zhiguo
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States IEEE 01.12.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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ISSN:2168-2267, 2168-2275, 2168-2275
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Abstract The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope their investment policies to be with the not only high profit but also low risk. Managers and investors involved pursue their own interests which are partly conflicting with others. Stochastic game theory has been widely applied to multiperson noncooperative decision making problem of financial market. However, for the nonlinear stochastic financial system with random fluctuations, it still lacks an analytical or computational scheme to effectively solve the complex noncooperative game strategy design problem. In this paper, the stochastic multiperson noncooperative game strategy in cyber-financial systems is transformed to a multituple Hamilton-Jacobi-Isacc inequalities (HJIIs)-constrained multiobjective optimization problem (MOP). This HJIIs-constrained MOP solution is also found to be the Nash equilibrium solution of multiperson noncooperative game strategy in nonlinear stochastic financial systems. In order to simplify design procedure by the global linearization theory, a set of local linear systems are interpolated to approximate the nonlinear stochastic financial system so that the m-tuple HJIIs-constrained MOP for noncooperative game strategy of cyber-financial system could be converted to a linear matrix inequalities (LMIs)-constrained MOP. Finally, an LMIs-constrained multiobjective evolution algorithm is explored for effectively solving the multiperson noncooperative game strategy in cyber-financial systems. Two design examples are also given for the illustration of the design procedure and the performance validation of the proposed stochastic noncooperative investment strategy in the nonlinear stochastic financial systems.
AbstractList The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope their investment policies to be with the not only high profit but also low risk. Managers and investors involved pursue their own interests which are partly conflicting with others. Stochastic game theory has been widely applied to multiperson noncooperative decision making problem of financial market. However, for the nonlinear stochastic financial system with random fluctuations, it still lacks an analytical or computational scheme to effectively solve the complex noncooperative game strategy design problem. In this paper, the stochastic multiperson noncooperative game strategy in cyber-financial systems is transformed to a multituple Hamilton-Jacobi-Isacc inequalities (HJIIs)-constrained multiobjective optimization problem (MOP). This HJIIs-constrained MOP solution is also found to be the Nash equilibrium solution of multiperson noncooperative game strategy in nonlinear stochastic financial systems. In order to simplify design procedure by the global linearization theory, a set of local linear systems are interpolated to approximate the nonlinear stochastic financial system so that the m-tuple HJIIs-constrained MOP for noncooperative game strategy of cyber-financial system could be converted to a linear matrix inequalities (LMIs)-constrained MOP. Finally, an LMIs-constrained multiobjective evolution algorithm is explored for effectively solving the multiperson noncooperative game strategy in cyber-financial systems. Two design examples are also given for the illustration of the design procedure and the performance validation of the proposed stochastic noncooperative investment strategy in the nonlinear stochastic financial systems.
The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope their investment policies to be with the not only high profit but also low risk. Managers and investors involved pursue their own interests which are partly conflicting with others. Stochastic game theory has been widely applied to multiperson noncooperative decision making problem of financial market. However, for the nonlinear stochastic financial system with random fluctuations, it still lacks an analytical or computational scheme to effectively solve the complex noncooperative game strategy design problem. In this paper, the stochastic multiperson noncooperative game strategy in cyber-financial systems is transformed to a multituple Hamilton-Jacobi-Isacc inequalities (HJIIs)-constrained multiobjective optimization problem (MOP). This HJIIs-constrained MOP solution is also found to be the Nash equilibrium solution of multiperson noncooperative game strategy in nonlinear stochastic financial systems. In order to simplify design procedure by the global linearization theory, a set of local linear systems are interpolated to approximate the nonlinear stochastic financial system so that the m-tuple HJIIs-constrained MOP for noncooperative game strategy of cyber-financial system could be converted to a linear matrix inequalities (LMIs)-constrained MOP. Finally, an LMIs-constrained multiobjective evolution algorithm is explored for effectively solving the multiperson noncooperative game strategy in cyber-financial systems. Two design examples are also given for the illustration of the design procedure and the performance validation of the proposed stochastic noncooperative investment strategy in the nonlinear stochastic financial systems.The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope their investment policies to be with the not only high profit but also low risk. Managers and investors involved pursue their own interests which are partly conflicting with others. Stochastic game theory has been widely applied to multiperson noncooperative decision making problem of financial market. However, for the nonlinear stochastic financial system with random fluctuations, it still lacks an analytical or computational scheme to effectively solve the complex noncooperative game strategy design problem. In this paper, the stochastic multiperson noncooperative game strategy in cyber-financial systems is transformed to a multituple Hamilton-Jacobi-Isacc inequalities (HJIIs)-constrained multiobjective optimization problem (MOP). This HJIIs-constrained MOP solution is also found to be the Nash equilibrium solution of multiperson noncooperative game strategy in nonlinear stochastic financial systems. In order to simplify design procedure by the global linearization theory, a set of local linear systems are interpolated to approximate the nonlinear stochastic financial system so that the m-tuple HJIIs-constrained MOP for noncooperative game strategy of cyber-financial system could be converted to a linear matrix inequalities (LMIs)-constrained MOP. Finally, an LMIs-constrained multiobjective evolution algorithm is explored for effectively solving the multiperson noncooperative game strategy in cyber-financial systems. Two design examples are also given for the illustration of the design procedure and the performance validation of the proposed stochastic noncooperative investment strategy in the nonlinear stochastic financial systems.
Author Yang , Chun-Tao
Chen, Wei-Yu
Chen, Bor-Sen
Yan, Zhiguo
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Snippet The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope...
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SubjectTerms Cyber-financial system
Decision making
Decision theory
Design engineering
Economic models
Evolutionary algorithms
Evolutionary computation
Game theory
Investment strategy
Linear matrix inequalities
Linear systems
Linearization
Markets
Mathematical analysis
Matrix methods
multiobjective evolutionary algorithm (MOEA)
multiobjective optimization problem (MOP)
multiperson noncooperative decision making
Multiple objective analysis
Nash equilibrium
Nash equilibrium solution
Nonlinear systems
stochastic noncooperative game strategy
Stochastic processes
Stochastic systems
System effectiveness
Variation
Title Noncooperative Game Strategy in Cyber-Financial Systems With Wiener and Poisson Random Fluctuations: LMIs-Constrained MOEA Approach
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