最大化生存概率的投资策略

Optimal Investment for Maximizing the Survival Probability

本文研究最大化生存概率准则下的最优投资问题。假设投资者面临着不可对冲的随机风险,市场是不完备的,任何投资策略都不能完全消除财富总量的下行风险。本文主要结果是:假设无风险资产利率大于零,分别研究了无借贷约束和有借贷约束条件下基于最大化生存概率准则的最优投资问题,运用随机控制理论,通过求解HJB方程,获得了最优投资策略及相应最大生存概率的闭式解,给出了数值算例,通过比较静态分析揭示了生存概率和投资策略与各参数之间的数量关系。结果表明,风险资产最优投资比例随财富总量的增加而减少,企业的生存概率随财富总量的增加而增加,随法定水平的增加而减少。

In this paper, we study the problem of optimal investment based on the criteria of maximizing probability of survival. On the assumption that investor is faced with a random risk process, the market is incomplete, and the risk of going down-side to the investor cannot be completely eliminated no matter what the investment strategy is. The main contributions are summed up as follows： Based on the maximizing probability of survival, we consider the optimal problem with and without the restriction of borrowing respectively if the risk-free is greater than zero. The closed-form expressions of the optimal strategy and the optimal value function are derived via solving the corresponding HJB equation. In addition, the comparative static analysis is presented, which explains the quantitative relations among the parameters, survival probability and investment strategy. The results indicate that the proportion invested in the risk asset decreases as the wealth level increases. The more the amount of wealth or the less the given goal level, the greater the survival probability.