Viscosity solutions for second order integro-differential equations without monotonicity conditions: The Probabilistic Approach

2014/11/09 by Marie-Amélie Morlais, Morlais, Marie-Amélie, Saïd Hamadène +2
Economics, Econometrics and Finance · Mathematics · #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.AP #msc:60H30

paper · pdf · doi:10.48550/arxiv.1411.2266

15 pages

openalex publication_date 2014/11/09 · arxiv created 2015/05/11 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish a new uniqueness result of a (continuous) viscosity solution for some integro-partial differential equation (IPDE in short). The novelty is that we relax the so-called monotonicity assumption on the driver, assumption which is classically assumed in the literature of viscosity solution of equation with a non local term. Our method strongly relies on the link between IPDEs and backward stochastic differential equations (BSDEs in short) with jumps for which we already know that the solution exists and is unique. In the second part of the paper, we deal with the IPDE with obstacle and we obtain similar results.

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