马尔可夫市场中的一般多期均值-方差资产负债管理问题的时间一致策略

葛浩,李仲飞

系统科学与数学 ›› 2019, Vol. 39 ›› Issue (10) : 1609-1631.

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PDF(624 KB)
系统科学与数学 ›› 2019, Vol. 39 ›› Issue (10) : 1609-1631. DOI: 10.12341/jssms13705
论文

马尔可夫市场中的一般多期均值-方差资产负债管理问题的时间一致策略

    葛浩1,2,李仲飞3
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Time-Consistent Strategy for General Multi-Period Mean-Variance Asset-Liability Management in a Markov Market

    GE Hao 1,2,LI Zhongfei3
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摘要

文章在多期均值-方差框架下研究一个带马尔可夫机制转换及跨期目标控制的一般资产负债管理问题. 随机的风险资产收益率和外生负债增长率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. 在投资过程中投资者不仅要考虑终端盈余的均值-方差效用,还需要同时关注中间目标效用的控制. 以最大化每时刻盈余的均值-方差效用的加权总和为目标,文章构建了一般的多期均值-方差资产负债管理模型. 在博弈论框架下,利用逆向归纳法,文章导出了问题的时间一致策略、均衡值函数及时间一致策略下每时刻盈余的期望和方差的解析表达式,并讨论了几种退化情形下的均衡结果. 最后,文章通过数值例子揭示了机制转换、负债对均衡有效前沿的影响以及跨期目标控制对资产负债管理的作用.

Abstract

This paper considers a multi-period mean-variance asset-liability management problem with regime switching and intertemporal restrictions. The random returns of risky assets and exogenous liability all depend on the states of a stochastic market which are assumed to follow a discrete-time Markov chain. Investors not only consider the mean-variance utility of final surplus, but also pay attention to intermediate restrictions on the portfolio during the investment process. With the goal of maximizing the weighted sum of the mean-variance utility of the surplus at each time, we construct a general mean-variance asset-liability management model. Within a game theoretic framework, we derive the time-consistent strategy, equilibrium value function and the expectation and variance of surplus at each time under the time-consistent strategy 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 and liability on the equilibrium effective frontier, as well as intertemporal restrictions on asset-liability management.

关键词

马尔可夫机制转换 / 跨期目标控制 / 多期均值-方差资产负债管理 / 时间一致策略 / 均衡有效前沿.

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葛浩 , 李仲飞. 马尔可夫市场中的一般多期均值-方差资产负债管理问题的时间一致策略. 系统科学与数学, 2019, 39(10): 1609-1631. https://doi.org/10.12341/jssms13705
GE Hao , LI Zhongfei. Time-Consistent Strategy for General Multi-Period Mean-Variance Asset-Liability Management in a Markov Market. Journal of Systems Science and Mathematical Sciences, 2019, 39(10): 1609-1631 https://doi.org/10.12341/jssms13705
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