The Study Of A Class Of Singular Stochastic Control With Discretionary Stopping Model

Stochastic optimal control is a important branch of control theory. In recent years, stochastic optimal control is widely and successfully applied in many fields. For example, spaceship navigation, antenna orientation, tracing problem, storage problem, risk control and production consumption research in economy.The research of stochastic optimal control is commenced in 1950s and 1960s, and developed in 1970s and 1980s.Many models is put forward and researched. The research of those models mainly divided into two aspects the research of stochastic differential equation (or integral equation) and the research of variation equation.This paper is mainly researched a class of singular stochastic control problem with stopping time which is put forward by M.H.Davis and M.Zerros in 1994.They proved that there are two kinds of optimal control strategies for this kind of model, that is 'reflecting and absorbing' optimal control and 'fail-stop' optimal stochastic control strategies. But its cost function and state construction is too simple to be used. In this paper the 'fail-stop' optimal control strategy is studied and its cost function and state construction is modified. In the end, we also discuss the key work which dissolve this kinds of problem, the construct and analysis of variation equation.This paper includes five chapters: The first chapter is the summary. The second chapter is the introduction of stochastic control and stochastic optimal control. The third chapter is the research of a class of ' fail—stop' optimal stochastic control strategy. The forth chapter is the discussion of several problems in some papers about stochastic control. The fifth chapter is the discussion of conditional regressive independent and conditional independence.