Existence, uniqueness and strict comparison theorems for backward stochastic differential equations driven by RCLL martingales

2021/03/16 by Tianyang Nie, Nie, Tianyang, Marek Rutkowski +1
Economics, Econometrics and Finance · Engineering · #60H10 #60H30 #91G30 #91G40 #Credit Risk and Financial Regulations #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2103.08898

openalex publication_date 2021/03/16 · openalex created_date 2021/03/29 · openalex updated_date 2026/07/28

Abstract

Results on the existence, uniqueness and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are established. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models with jumps, including as particular cases the setups studied by Peng and Xu \citePX2009,PX2010 and Dumitrescu et al. \citeDGQS2018 who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump.

Citations

• Quadratic Exponential Semimartingales and Application to BSDEs with jumps
• Arbitrage-free pricing of American options in nonlinear markets

Related

• Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales
• BSDEs with default jump
• Backward Stochastic Differential Equations in Financial Mathematics
• Solvability of Backward Stochastic Differential Equations with Quadratic Growth
• Comparison theorems for multi-dimensional BSDEs with jumps and applications to constrained stochastic linear-quadratic control