Diagonally quadratic BSDE with oblique reflection and optimal switching

TL;DR

This paper investigates diagonally quadratic backward stochastic differential equations with oblique reflection, establishing existence, uniqueness, and applications to risk-sensitive switching problems in stochastic control.

Contribution

It introduces a penalization method to prove existence and uniqueness of solutions for these complex BSDEs, extending their applicability to stochastic switching problems.

Findings

Existence of solutions via penalization approach

Uniqueness confirmed through value characterization

Application to risk-sensitive stochastic switching problems

Abstract

The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence fo a solution by providing some delicated a priori estimates. We further obtain the uniqueness by verifying the first component of the solution is indeed the value of a switching probelm for quadratic BSDEs. Moreover, we provide an extension for the solvability and apply our results to study a risk-sensitive switching problem for functional stochastic differential equations.