Reflected generalized BSDEs with random time and applications

TL;DR

This paper studies solutions to reflected generalized backward stochastic differential equations with random time horizons, establishing existence and uniqueness, and applies these results to American option pricing and obstacle problems for PDEs.

Contribution

It introduces new existence and uniqueness results for reflected generalized BSDEs with random time, and applies them to financial and PDE obstacle problems.

Findings

Established existence and uniqueness of solutions for reflected generalized BSDEs.

Derived a probabilistic formula for viscosity solutions of obstacle PDEs.

Applied results to American option pricing with infinite horizon.

Abstract

In this paper, we aim to study solutions of reflected generalized BSDEs, involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary. We consider both a finite random terminal and a infinite horizon. In both case, we establish an existence and uniqueness result. Next, as an application, we get an American pricing option in infinite horizon and we give a probabilistic formula for the viscosity solution of an obstacle problem for elliptic PDEs with a nonlinear Neumann boundary condition.