# A Direct Method for Solving Optimal Switching Problems of One-Dimensional Diffusions

## TL;DR

This paper introduces a direct, conjecture-free method for solving optimal switching problems in one-dimensional diffusions, leveraging a theory of optimal stopping and linear majorants.

## Contribution

It presents a novel direct approach that avoids the need for conjectures or proofs via quasi-variational inequalities in optimal switching problems.

## Key findings

- The method effectively characterizes the value function using linear majorants.
- It simplifies solving optimal switching problems without assuming the form of the solution.
- The approach is applicable to a broad class of one-dimensional diffusion models.

## Abstract

In this paper, we propose a direct solution method for optimal switching problems of one-dimensional diffusions. This method is free from conjectures about the form of the value function and switching strategies, or does not require the proof of optimality through quasi-variational inequalities. The direct method uses a general theory of optimal stopping problems for one-dimensional diffusions and characterizes the value function as sets of the smallest linear majorants in their respective transformed spaces.