Optimal Switching under Ambiguity and Its Applications in Finance

TL;DR

This paper investigates optimal switching strategies under ambiguity using multidimensional RBSDEs, revealing how ambiguity influences decision-making in finite and infinite horizon financial models.

Contribution

It introduces a novel characterization of optimal switching under ambiguity via multidimensional RBSDEs, extending the analysis to infinite horizons and highlighting the impact of ambiguity.

Findings

Optimal switching value function matches solutions to multidimensional RBSDEs.

Ambiguity alters the structure of optimal switching strategies.

Extension from finite to infinite horizon problems.

Abstract

In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and show that a value function of the optimal switching under ambiguity coincides with a solutions to multidimensional RBSDEs with allowing negative switching costs. Furthermore, we naturally extend the finite horizon problem to the infinite horizon problem. In some applications, we show that ambiguity affects an optimal switching strategy with the different way to a usual switching problem without ambiguity.