\mathbbL^p (p>1)-solutions for BSDEs with jumps and stochastic monotone generator

2025/02/01 by Badr Elmansouri, Elmansouri, Badr, Mohamed El Otmani +1
Decision Sciences · Economics, Econometrics and Finance · #60H10 #60H15 #60H30 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2502.00371

openalex publication_date 2025/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study multidimensional discontinuous backward stochastic differential equations in a filtration that supports both a Brownian motion and an independent integer-valued random measure. Under suitable \mathbbL^p-integrability conditions on the data, we establish the existence and uniqueness of \mathbbL^p-solutions for both cases: p ≥ 2 and p ∈ (1,2). The generator is assumed to be stochastically monotone in the state variable y, stochastically Lipschitz in the control variables (z, u), and to satisfy a stochastic linear growth condition, along with an appropriate \mathbbL^p-integrability requirement.

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