Cash management decision with probability criterion

A mathematical model for the problem of multiperiod cash management is established. The problem is based on a discrete stochastic dynamic system and the decision criterion is a probability criterion. It is to maximize the probability that the investment gain rate is no less than a given expected gain rate in every period. Since this problem is an optimal control problem of a discrete stochastic system and more complex than the classical optimal control problem, the criterion function can not be calculated by analytic formulation. The traditional solving techniques are no longer valid. In this paper, a method of computing the value of the criterion function by stochastic simulation is presented, and a method based on the genetic algorithm for solving this multiperiod cash management problem is provided. Finally, the steps of the stochastic simulation based genetic algorithm are listed and an illustration example is given