Solution of a two-dimensional stochastic investment problem

摘要

This paper gives an extension of the work of Kobila [Stochastics Stochastic Rep. 43 (1993) 29–63]. The one-dimensional stochastic differential equation considered in that paper is now extended to two dimensions. The resultant partial differential equation is solved by a finite difference method. Therefore, there exists a two-dimensional stochastic investment problem whose solution could be solved, at least numerically.