带交易成本的时间一致风险控制与投资策略  

Time-Consistent Risk Control and Investment Strategies With Transaction Costs

作　　者：王彦凯 彭幸春 Wang Yankai;Peng Xingchun(School of Science,Wuhan University of Technology,Wuhan 430070)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《数学物理学报（A辑）》2024年第5期1400-1414,共15页Acta Mathematica Scientia

基　　金：教育部人文社科基金(22YJAZH087)。

摘　　要：该文在保险公司的最优风险控制与投资问题中考虑二次型形式的交易成本,并且假设保险市场和金融市场是相关的.在动态均值-方差准则下,通过求解扩展的HJB方程组获得了均衡策略以及值函数,它们依赖于一个矩阵Riccati方程组的解最后,通过一些数值算例,分析了交易成本水平和市场相关系数对均衡策略和有效前沿的影响.结果表明,随着交易成本水平或市场相关系数的增加,投资的增长率会减小.并且交易成本水平的增加会导致有效前沿的下降。This paper incorporates quadratic transaction costs in the optimal risk control and invest-ment problem for an insurer.Moreover,suppose that the insurance and financial markets are correlated.Under the dynamic mean-variance criterion,by solving a system of extended HJB equations,the e-quilibrium risk control and investment strategies and the corresponding value function are derived in terms of the solution to a system of matrix Riccati equations.Finally,the effects of transaction costs level and the market correlation coeficient on the equilibrium strategy and the efficient frontier are analyzed by some numerical examples.It turns out that the growth rate of investment slows down as the transaction costs level or the correlation coeficient increases,and the increase of transaction costs level will lead to the decrease of the efficient frontier.

关 键 词：交易成本 市场相关性 风险控制 投资 时间一致性 

分 类 号：O211.6[理学—概率论与数理统计]