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研究了Heston随机波动率模型下带有负债过程的动态投资组合问题,并且假设风险资产价格过程满足Heston随机波动率模型,负债过程服从带漂移的布朗运动.金融市场由一种无风险资产和一种风险资产所构成.首先,应用动态规划原理得到相应值函数所满足的HJB方程.然后,假设投资者对风险的偏好程度满足双曲绝对风险厌恶(HARA)效用函数,并应用Legendre变换法和分离变量法得到在HARA效用函数下最优投资策略的显示解.最后,给出数值算例分析部分市场参数对最优投资策略的影响.
We study the dynamic portfolio with liability process under Heston stochastic volatility model and assume that the risk asset price process satisfies the Heston stochastic volatility model and the debt process obeys the Drift Brownian motion.The financial market consists of a risk- Which is composed of risk assets.Firstly, the HJB equation, which is satisfied by the corresponding value function, is obtained by using the principle of dynamic programming.Furthermore, assuming the investor’s preference degree of risk satisfies the hyperbolic absolute risk aversion (HARA) utility function, and applying Legendre transform method and The method of separating variables to get the display solution of the optimal investment strategy under the HARA utility function.Finally, numerical examples are given to analyze the influence of some market parameters on the optimal investment strategy.