多阶段均值–方差资产负债管理的随机控制

Stochastic control for multiperiod mean-variance asset-liability management

中文关键词  多期投资组合  随机控制  资产负债管理  平均场方法  金融应用

英文关键词  multiperiod portfolio optimization  stochastic control systems  asset-liability management  mean-field formulation  finance applications

中文摘要

      资产负债管理研究如何合理分配资产以到达最小化风险同时确保期望剩余财富(财富减去负债)达到一定水平.本文在均值–方差投资组合理论的框架下研究两类资产负债管理模型, 包括带有跨期均值–方差投资目标和带有非破产约束的模型. 由于在动态规划意义下, 方差不具有可分性质, 传统的随机最优控制方法难以直接应用. 如采用处理动态均值–方差优化问题的嵌入法来解决以上问题会带来计算上的困难. 本文借鉴平均场控制的思想对以上两类问题加以研究. 本文假设了非常宽泛的市场模型: 所有的资产都是风险资产; 债务和风险资产之间存在相关性. 在此市场假设模型下, 本文给出了最优投资策略(控制率)的解析表达式和均值–方差有效前沿的表达形式. 本研究成果为投资者提供了新的投资策略, 可应用于更复杂的资产负债管理中.

英文摘要

      The objective of asset and liability management (ALM) is to seek an optimal portfolio policy such that a risk measure (variance of the surplus) is minimized while achieving a certain threshold level for the expected value of the surplus. This paper studies two multiperiod mean-variance-based ALM models including the one with intertemporal risk control and the other one with no bankruptcy restriction. Due to the nonseparability of the variance, it is hard to solve this problem by stochastic control approach directly. Instead of adopting the widely used embedding method which may encounter computational difficulty in solving these problems, we develop a novel stochastic control approach of a mean-field type. Under a general market assumption, the analytical portfolio policies and mean-variance efficient frontiers are derived for these two ALM problems. The new result developed in this paper provides investors with efficient ways in characterizing their optimal portfolio and liability management strategies for these sophisticated mean-variance-based ALM models.