Dynamic programming for discrete-time finite horizon optimal switching problems with negative switching costs

TL;DR

This paper extends dynamic programming methods to solve finite-horizon optimal switching problems with both positive and negative switching costs, using a martingale approach to handle signed costs.

Contribution

It introduces an explicit dynamic programming approach for problems with signed switching costs, expanding the applicability of existing methods.

Findings

Extended dynamic programming method for signed costs

Validated approach through theoretical analysis

Applicable to a broader class of switching problems

Abstract

This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal stopping problems, we extend a well known explicit dynamic programming method for computing the value function and the optimal strategy to the case of signed switching costs.