CIR利率模型下基于二次效用的资产–负债管理模型

Asset and Liability Management Model with CIR Interest Rate under Quadratic Utility Criterion

应用动态规划原理和Legendre变换相结合的方法研究CIR利率模型下的资产–负债管理问题.假设金融市场由一种无风险资产、多种风险资产和一种零息票债券构成,其中短期利率的动态行为服从Cox-Ingersoll-Ross(CIR)利率模型,而负债的动态行为满足带漂移的布朗运动,且负债动态与股票价格动态存在相关性.文章以最大化终端财富的期望效用为目标函数,应用变量替换方法得到二次效用下最优投资策略的闭式解,并给出数值算例分析利率参数和负债参数对最优投资策略的影响.研究结果解决了均值–方差模型下的最优投资策略问题,为进一步分析和研究随机利率模型下的其它资产–负债管理问题提供了理论支持.数值结果表明:负债情形下投资于股票和零息票债券的数量多于无负债情形下的数量.

This paper applies dynamic programming principle and Legendre transform to study an asset and liability management problem with CIR interest rate dynamics. Assume that the finance market is composed of one risk-free asset and multiple risky assets and one zero-coupon bond, where the interest rate is supposed to follow the CIR model and the liability process is driven by Brownian motion with drift, moreover, liability dynamics is generally correlated with stock price dynamics. The aim of an investor is to maximize the expected utility of terminal wealth. The closed-form solution to the optimal investment strategy under the quadratic utility case is obtained by applying the variable change technique, and a numerical example is given to illustrate the impact of interest rate parameters and liability parameters on the optimal policy. We obtain the optimal investment policy in the mean-variance framework and further provide theoretical foundation for other asset and liability management problems with stochastic interest rates. The numerical results imply that the amount invested in the stocks and zero-coupon bond in the liability setting is larger than that in the no-liability setting.