Adomian's Decomposition Method Applied to an Exponential Equation

The purpose of this study is to obtain a decomposition of the solution to a backward stochastic differential equation used in the dual problem of mathematical finance. Some explicitly solvable equations considered. We convert the equation into a system of recurrent relations. By solving this system and proving convergence of the series the solution to the equation can be determined. In this study, Adomian's method was applied to solve the backward stochastic differential equation. An explicit solution was obtained for some examples.