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.

中文翻译：

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具有维纳和泊松随机波动的网络金融系统中的非合作博弈策略：LMIs 约束的 MOEA 方法


金融市场是一个具有连续维纳和不连续泊松随机波动的非线性随机系统。大多数管理者或投资者都希望他们的投资政策不仅是高利润而且是低风险。所涉及的管理者和投资者追求自己的利益，而这些利益与他人存在部分冲突。随机博弈论已广泛应用于金融市场多人非合作决策问题。然而，对于具有随机波动的非线性随机金融系统，仍然缺乏有效解决复杂非合作博弈策略设计问题的解析或计算方案。本文将网络金融系统中的随机多人非合作博弈策略转化为多重 Hamilton-Jacobi-Isacc 不等式 (HJII) 约束的多目标优化问题 (MOP)。这种 HJII 约束的 MOP 解也被发现是非线性随机金融系统中多人非合作博弈策略的纳什均衡解。为了利用全局线性化理论简化设计过程，通过插值一组局部线性系统来逼近非线性随机金融系统，从而将网络金融系统非合作博弈策略的m元组HJII约束MOP转换为线性矩阵不等式 (LMI) 约束的 MOP。最后，探索了一种 LMI 约束的多目标进化算法，以有效解决网络金融系统中的多人非合作博弈策略。 还给出了两个设计实例来说明非线性随机金融系统中所提出的随机非合作投资策略的设计过程和性能验证。