Progressive enlargement of filtrations and Backward SDEs with jumps

2011/01/14 by Idris Kharroubi, Kharroubi, Idris, Thomas Lim +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Credit Risk and Financial Regulations #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1101.2815

openalex publication_date 2011/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work deals with backward stochastic differential equation (BSDE) with random marked jumps, and their applications to default risk. We show that these BSDEs are linked with Brownian BSDEs through the decomposition of processes with respect to the progressive enlargement of filtrations. We show that the equations have solutions if the associated Brownian BSDEs have solutions. We also provide a uniqueness theorem for BSDEs with jumps by giving a comparison theorem based on the comparison for Brownian BSDEs. We give in particular some results for quadratic BDSEs. As applications, we study the pricing and the hedging of a European option in a complete market with a single jump, and the utility maximization problem in an incomplete market with a finite number of jumps.

Citations

• Utility maximization in incomplete markets
• A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem

Cited by

• L^p solution of backward stochastic differential equations driven by a\n marked point process

Related

• BSDEs with default jump
• Robustness of quadratic hedging strategies in finance via backward stochastic differential equations with jumps
• Backward Stochastic Differential Equations in Financial Mathematics
• A New Class of Backward Stochastic Partial Differential Equations with Jumps and Applications
• D-solutions of BSDEs with Poisson jumps