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  

Time-Consistent Strategy for General Multi-Period Mean-Variance Asset-Liability Management in a Markov Market

作　　者：葛浩 李仲飞[3] GE Hao;LI Zhongfei(School of Mathematics,Sun Yat-sen University,Guangzhou 510275;School of Computer Science and Technology,Dongguan University of Technology,Dongguan 523808;Sun Yat-sen Business School,Sun Yat-sen University,Guangzhou 510275)

机构地区：[1]中山大学数学学院,广州510275 [2]东莞理工学院计算机科学与技术学院,东莞523808 [3]中山大学管理学院,广州510275

出　　处：《系统科学与数学》2019年第10期1609-1631,共23页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金创新研究群体项目(71721001);广东省自然科学基金研究团队项目(2014A030312003)资助课题

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.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 

分 类 号：F83[经济管理—金融学]