Models for the First Arrival Target Distribution Function Optimization and Risk Minimization in Discrete Time

摘要

This article thoroughly investigates the problems concerning the optimal models for the first arrival target distribution function in discrete time. Various properties of the optimal policies and the optimal objective function are presented. The risk uniform minimization problems are discussed in detail as a special case. The optimality equation and a necessary and sufficient condition of optimality are also obtained. Furthermore, an effective algorithun is developed tp find the optimal objective function and the optimal policies. Some preliminary results about the relationship between the parameters and the optimality are given.