A boundary value problem for a non-linear difference equation

Abstract

A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented.

Keywords

• higher-order difference equations
• optimal control
• dynamic programming
• first-passage time
• homing problem