On stochastic optimal control and its applications in finance

Applications of stochastic optimal control to management and finance problems were developed from 1970s,. The dynamic programming approach provides a characterization of the value function and optimal control. In this paper we present the stochastic optimal control formulation and concentrate on some applications in financial mathematics [3,4]. Using dynamic programming, we obtain the dynamic programming approach that in general we can’t solve it analytically. Many problems in financial mathematics involve the solution of stochastic optimal control (SOC) problems. In this work, the variational iteration method (VIM) is applied for solving SOC problems. In fact, solutions for the value function and the corresponding optimal strategies are obtained numerically. We solve a stochastic linear regulator problem to investigate the applicability and simplicity of the presented method and prove its convergence. In particular, for Merton’s portfolio selection model as a problem of portfolio optimization, the proposed numerical method is applied for the first time and its usefulness is demonstrated. For the nonlinear case, we investigate its convergence using Banach’s fixed point theorem. The numerical results confirm the simplicity and efficiency of our method.