Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games

TL;DR

This paper introduces a new class of reflected backward stochastic differential equations with two cadlag barriers that do not require separation conditions, leading to solutions that are generally not semimartingales, with applications to Dynkin games and variational inequalities.

Contribution

It develops existence, uniqueness, and approximation results for a novel class of reflected BSDEs without semimartingale solutions, broadening the scope of stochastic differential equations.

Findings

Solutions are not semimartingales in general.

Existence and uniqueness are established for the new class.

Applications to Dynkin games and variational inequalities are demonstrated.

Abstract

We introduce a new class of reflected backward stochastic differential equations with two c\`adl\`ag barriers, which need not satisfy any separation conditions. For that reason, in general, the solutions are not semimartingales. We prove existence, uniqueness and approximation results for solutions of equations defined on general filtered probability spaces. Applications to Dynkin games and variational inequalities, both stationary and evolutionary, are given.