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假设无风险利率可由Ho-Lee利率模型描述,且与股票动态存在一般线性相关系数,应用最优性原理和HJB方程研究了市场存在多种风险资产情形的动态资产分配问题,通过变量替换方法得到了幂效用和指数效用下最优投资策略的显示解,数值算例分析了利率参数和市场参数对最优投资策略的影响趋势。研究结果发现:两种效用下的最优策略均由两部分所构成,一部分由市场参数所确定,另一部分由利率参数所确定。而且,幂效用下的最优投资策略与瞬时利率无关,而指数效用下的最优投资策略与瞬时利率相关。
Assuming that the risk-free interest rate can be described by the Ho-Lee interest rate model, and there is a general linear correlation coefficient with the stock dynamics, we apply the optimality principle and the HJB equation to study the dynamic asset allocation problem with multiple risky assets in the market. The power solution and exponential utility show the optimal solution to the investment strategy. Numerical examples analyze the effect of interest rate parameters and market parameters on the optimal investment strategy. The result shows that the optimal strategy under two kinds of utility consists of two parts, one is determined by the market parameters and the other is determined by the interest rate parameters. Moreover, the optimal investment strategy under the exponential utility has nothing to do with the instantaneous interest rate, while the optimal investment strategy under the exponential utility is related to the instantaneous interest rate.