On the One-Dimensional Optimal Switching Problem

TL;DR

This paper provides an explicit solution to the one-dimensional optimal switching problem using dynamic programming and properties of concave functions, clarifying the structure of the value function.

Contribution

It introduces a direct method for solving the problem by exploiting the excessive characterization and shape properties of the value function.

Findings

Explicit solution for one-dimensional switching problem

Value function characterized by concavity and smooth fit

Method applicable to similar stochastic control problems

Abstract

We explicitly solve the optimal switching problem for one-dimensional diffusions by directly employing the dynamic programming principle and the excessive characterization of the value function. The shape of the value function and the smooth fit principle then can be proved using the properties of concave functions.