Discrete-time risk-aware optimal switching with non-adapted costs

TL;DR

This paper addresses non-Markovian, risk-aware optimal switching problems in discrete time, establishing theoretical foundations and demonstrating applicability to hydropower planning.

Contribution

It introduces a framework for solving non-Markovian risk-aware switching problems and proves existence and uniqueness of solutions for related reflected backward stochastic difference equations.

Findings

Established existence and uniqueness of solutions.

Applied the theory to hydropower planning.

Extended the framework to general filtrations.

Abstract

We solve non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk aware and the filtration is general, and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations. An example application to hydropower planning is provided.