具有线性消费模式的最优投资研究

Study of Optimal Investment with Linear Consumption

本文研究线性消费模式的最优投资问题。不同于Merton问题中消费是内生决策变量,本文假设投资者单位时间内必须消费不少于一个固定数量的财富,因而投资者有可能最终破产。在两类不同投资目标下,通过求解模型相对应的HJB方程,都获得了最优投资策略及最优值函数的闭式解。结果表明,最大化终止时刻财富期望效用准则的最优投资策略与最小化破产概率准则的最优投资策略截然不同。

In this paper we study the problem of optimal investment with linear consumption. Different from Merton problem which consumption is a decision variable, there is a positive probability of ruin because investor is forced to pay more than a fixed quantity of money per unit time. Under two different criteria we get closed-form expressions of the optimal strategies and the optimal value functions by solving the corresponding HJB equation in each ease. The results indicate that the optimal strategies are completely different between based on maximizing expected utility criteria and minimizing ruin probability criteria.