Robust portfolio selection has become a popular problem in recent years. In this paper, we study the optimal investment problem for an individual who carries a constant consumption rate but worries about the model ambiguity of the financial market. Instead of using a conventional value function such as the utility of terminal wealth maximization, here, we focus on the purpose of risk control and seek to minimize the probability of lifetime ruin. This study is motivated by the work of Bayraktar and Zhang (2015), except that we use a standardized penalty for ambiguity aversion. The reason for taking a standardized penalty is to convert the penalty to units of the value function, which makes the difference meaningful in the definition of the value function. The advantage of taking a standardized penalty is that the closed-form solutions to both the robust investment policy and the value function can be obtained. By employing the dynamic programming principle, we derive the Hamilton-Jacobi-Bellman (HJB) equation satisfied by the value function, thereby obtaining the closed-form solutions for both the robust investment strategy and the value function. More interestingly, we use the “Ambiguity Derived Ratio” to characterize the existence of model ambiguity which significantly affects the optimal investment policy. Finally, several numerical examples are given to illustrate our results.
