关键词: Heston 随机波动率, 资产负债管理, 指数效用函数, 最优资产配置策略

Abstract: 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.

Key words: Heston stochastic volatility, asset liability management, exponential utility function, optimal asset allocation strategy