Chol-Gyu Pak | Searcharxiv

arXiv2019

Uniqueness, Comparison and Stability for Scalar BSDEs with {Lexp(μsqrt(2log(1+L)))}-integrable terminal values and monotonic generators

This paper considers a class of scalar backward stochastic differential equations (BSDEs) with $L\exp(μ\sqrt{2\log(1+L)})$-integrable terminal values. We associate these BSDEs with BSDEs with integrable parameters through Girsanov change. Using this technique, we prove uniqueness, comparisons and stability for them under an extended monotonicity condition (more precisely one sided Osgood condition).

math.PR↗

arXiv2019

Stochastic Gronwall's inequality in random time horizon and its application to BSDE

In this paper, we introduce and prove a stochastic Gronwall's inequality in (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under stochastic monotonicity condition.

math.PR↗