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. International Federation of Operational Research Societies 2002.