Maximum Principle of Optimal Stochastic Control with Terminal State Constraint and Its Application in Finance

摘要

This paper considers the optimal control problem for a general stochastic system with general terminal state constraint.Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type.The author puts forward two ways to understand the target set and the variation set.Then under two kinds of finite-codimensional conditions,the stochastic maximum principles are established,respectively.The main results are proved in two different ways.For the former,separating hyperplane method is used;for the latter,Ekeland's variational principle is applied.At last,the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.