Bounded solutions, L^p (p>1) solutions and L¹ solutions for one-dimensional BSDEs under general assumptions

2015/08/11 by Shengjun Fan, Fan, ShengJun · 5 citations
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Differential Equations and Numerical Methods #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1508.02501

Abstract

This paper aims at solving one-dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, L^p (p>1) solutions and L¹ solutions of the BSDEs. The time horizon is allowed to be finite or infinite, and the generator g is allowed to have a general growth in y and a quadratic growth in z. As compensation, the generator g needs to satisfy a kind of one-sided linear or super-linear growth condition in y, instead of the monotonicity condition in y as is usually done. Many of our results improve virtually some known results, even though for the case of the finite time horizon and the case of the L² solution.

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