A Hybrid Optimal Control Model

摘要

A hybrid variable is a mathematical notion used to describe a situation in which randomness and fuzziness simultaneously appear in a system. Based on this concept, a hybrid optimal control problem is presented and investigated. In order to examine this hybrid optimal control problem, we first derive the Bellman's Optimality Principle. The principle is then used to prove a fundamental result called the equation of optimality for hybrid optimal control. This last result is applied to solve a portfolio selection problem in which the price process for a stock is described by a hybrid differential equation.