带机制转换和随机现金流的多期均值-方差资产负债管理问题的均衡策略

Equilibrium Strategy for Multi-Period Mean-Variance Asset-Liability Management with Regime Switching and a Stochastic Cash Flow

文章在马尔可夫机制转换的市场及多期均值-方差框架下研究一个带随机现金流的资产负债管理问题的均衡投资策略.随机的风险资产收益率、外生负债增长率、风险厌恶系数和现金流均依赖于有限多个服从离散时间马尔可夫链的金融市场状态.在博弈论框架下,利用逆向归纳法,文章导出问题的均衡策略、均衡值函数以及均衡有效前沿的解析表达式.此外,文章讨论了几种退化情形下的均衡结果.最后,文章通过数值例子分别分析了机制转换、随机现金流、负债以及投资期限对均衡有效前沿的影响.

This paper studies the equilibrium investment strategy for a multi-period mean-variance asset-liability management problem with regime switching and a stochastic cash flow.In this model,not only the asset returns and exogenous liability returns,but also the risk aversion coefficient and cash flow depend on the stochastic market states,which are assumed to follow a discrete-time Markov chain.Within a game theoretic framework,we derive the equilibrium strategy,equilibrium value function and equilibrium effective frontier in closed-form by applying the backward induction approach.Several degenerate cases are discussed and numerical examples are given to demonstrate the effects of regime-switching,stochastic cash flow,liability and investment horizon T on the equilibrium effective frontier.