An investment decision model with the survival probability criterion and its numerical solutions: The finite horizon case

This paper studies a finite horizon investment decision model. Suppose that an investor is endowed with initial wealth in the beginning. At every stage, he needs to consume a part of his wealth and allocate the rest between a risky and a riskless asset. The investor wishes to maximize the survival probability that his wealth can satisfy the consumption requirements during the horizon and reach a disaster level at the end. Since the allocation decision depends on not only his wealth but also the disaster level, we introduce a Markov decision process based on decision space to describe the investment behavior of the investor and prove the existence of a deterministic Markov optimal policy. An algorithm to compute the optimal policy and the maximal probability of survival is given and four numerical examples are discussed.