基于Heston随机波动率模型和风险偏好视角的资产负债管理

本文研究基于Heston随机波动率模型的资产负债管理问题。假设金融市场由一个无风险资产和一个风险资产构成,投资者的目标是最大化其终端财富的期望效用。应用随机控制方法,得到了该问题最优资产配置策略的解析表达式和相应值函数的解析解,通过数值算例分析了Heston模型主要参数以及债务对最优资产配置策略的影响。结果表明:配置到风险资产的比例对Heston模型中的参数非常敏感;为了对冲债务风险,负债的引入使得配置到风险资产的比例比无负债情形下的高;在风险厌恶系数变大时,无论投资者是否有负债,其投资到风险资产的比例则越来越低。

Asset Liability Management Based on Heston Stochastic Volatility Model and Risk Preference

In this paper, we study an asset liability management problem under the Heston stochastic volatility market. We assume that the market is composed of a risk-free asset and a risky asset whose price process satisfies the Heston model, while the investor's goal is to maximize the expected utility of the terminal wealth. By using the stochastic control method, we obtain closed-form solutions to the optimal asset allocation strategy and the corresponding value function. Moreover, we present numerical examples to show the effects of model parameters and liabilities on the optimal asset allocation strategy. It is shown that: (1) The proportion to the risk asset is very sensitive to the parameters in the Heston model; (2) To hedge the risk of liability, the introduction of liability makes the proportion of investment in the risk asset much higher than the corresponding case without liability; (3) As the risk aversion coefficient becomes larger, the proportion of investment in the risk asset is much lower, no matter whether the investor has liabilities.