Reflected BSDE driven by a marked point process with a convex/concave generator

TL;DR

This paper studies a class of reflected backward stochastic differential equations driven by marked point processes with convex or concave generators, establishing their well-posedness and applying them to American option pricing.

Contribution

It introduces a novel approach to analyze RBSDEs driven by marked point processes with unbounded conditions and demonstrates their application in financial option pricing.

Findings

Proved well-posedness of RBSDEs with unbounded terminal conditions.

Developed a method for solving American options via utility maximization.

Applied fixed point, θ-method, and truncation techniques to RBSDEs.

Abstract

In this paper, a class of reflected backward stochastic differential equations (RBSDE) driven by a marked point process (MPP) with a convex/concave generator is studied. Based on fixed point argument, $\theta$-method and truncation technique, the well-posedness of this kind of RBSDE with unbounded terminal condition and obstacle is investigated. Besides, we present an application on the pricing of American options via utility maximization, which is solved by constructing an RBSDE with a convex generator.