A dynamic programming approach for investment problem with stochastic number of investment chances

This paper uses a dynamic programming (DP) approach to obtain the optimal policies for an investor who faces a stochastic number of investing chances (with Poisson distribution) and a stochastic profit for every chance occurring (with uniform distribution). First a model with deterministic number of investing chances is introduced. Then an approach is developed for obtaining optimal solutions for stochastic model using the concept of conditioning. For more clarity a numerical example is presented.