On The2-Dimensional SDE Based Optimal Switching Problem

In this paper we consider the optimal switching mechanism driven by2-dimensional stochastic differential equation. We try to convert a2-variable partial differential equation, which is acquired by the infinitesimal generator of the above stochastic differential equation, into a1-variable ordinary differential equations, by means of Taylor expansion. Then we obtain a new stochastic differential equation, and, with the boundary conditions involved, we get an approximative solution of the2-variable optimal switching mechanism, following existing methods for solving the1-variable optimal switching mechanism. The solution consists of the de-termination of approximative optimal value function and approximative optimal switching time, and the solvement of the stochastic dynamical programming, etc.