Two-barriers-reflected BSDE with Rank-based Data

TL;DR

This paper studies two-barriers-reflected backward stochastic differential equations driven by rank-based data, establishing their connection to obstacle problems in PDEs and applying this to American game option pricing.

Contribution

It introduces a novel analysis of two-barriers-reflected BSDEs with rank-based data and links their solutions to obstacle problems in PDEs, with applications to option pricing.

Findings

Established the probabilistic representation of viscosity solutions for obstacle PDEs.

Proved existence and uniqueness of solutions for the two-barriers-reflected BSDEs.

Applied the theoretical results to the pricing of American game options.

Abstract

We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations restricted to two prescribed upper-boundary and lower-boundary processes. We rigorously show that this solution gives a probabilistic expression to the viscosity solution of some obstacle problems for the corresponding parabolic partial differential equations. As an application, the pricing problem of an American game option is studied.