Solution of stochastic optimal control problems and financial applications

Abstract

In this paper, the stochastic optimal control problems, which frequently occur in economic and finance are investigated. First, using Bellman’s dynamic programming method the stochastic optimal control problems are converted to Hamilton-Jacobi-Bellman (HJB) equation. Then, obtained HJB equation is solved through the method of separation of variables by guessing a solution via its terminal condition. Also, the non-linear optimal feedback control law is constructed. Finally, the solution procedure is illustrated for solving some examples that two of them are financial models. In fact, to highlight the applications of stochastic optimal control problems in financial mathematics, some financial models are presented.