PDEs FOR REFLECTED BSDENMs APPLIED TO AMERICAN OPTIONS

Abstract

This paper studies the solution of a backward stochastic differential equation driven by normal martingale (BSDENM for short) with a right continuous and left limited lower obstacle (rcll for short) assuming a nondeterministic Lipschitz condition. We prove the existence and uniqueness of the solution via penalization methods with the help of the monotonic limit theorem and the Snell envelope theory. As for application, we discuss the fair valuation of American options and the connection between reflected BSDENM and partial differential equations (PDEs for short).