ABSTRACT

This paper investigates a dynamic continuous-time asset-liability management (ALM) problem with delay under the mean-variance criterion. The investor allocates her wealth in a financial market consisting of one risk-free asset and one risky asset, and she is subject to a random liability. The historical information of the wealth and liability affects the investor's wealth process, which is then governed by a stochastic differential delay equation. Firstly, a general ALM problem with delay is formulated and the extended Hamilton-Jacobi-Bellman system of equations is obtained. Secondly, we focus on a linear model and derive the closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function. Meanwhile, we also derive the pre-commitment strategy for the mean-variance ALM problem with delay using the maximum principle. Finally, some numerical examples and sensitivity analysis are presented to illustrate the equilibrium investment strategies and the efficient frontiers under the equilibrium and pre-commitment frameworks.

摘要

本文研究了在均方差准则下具有延迟的动态连续时间资产负债管理 (ALM) 问题。投资者在一个由一种无风险资产和一种风险资产组成的金融市场中分配她的财富，并且她承担着随机负债。财富和负债的历史信息影响投资者的财富过程，然后由随机微分延迟方程控制。首先，建立了一个具有延迟的一般ALM问题，并得到了扩展的Hamilton-Jacobi-Bellman方程组。其次，我们关注一个线性模型，推导出均衡投资策略的闭式表达式和相应的均衡价值函数。同时，我们还使用最大原理推导出了具有延迟的均值方差 ALM 问题的预承诺策略。最后，给出了一些数值例子和敏感性分析来说明均衡和预承诺框架下的均衡投资策略和有效边界。