Minimal supersolutions of BSDEs under volatility uncertainty

TL;DR

This paper investigates the existence of minimal supersolutions of backward stochastic differential equations (BSDEs) under volatility uncertainty, considering generators with specific regularity and structural properties across a family of mutually singular probability measures.

Contribution

It establishes conditions for the existence of minimal supersolutions of BSDEs under a family of mutually singular measures, extending the theory to more general settings.

Findings

Existence of minimal supersolutions under certain generator conditions

Extension of BSDE theory to volatility uncertainty scenarios

Framework accommodating mutually singular probability measures

Abstract

We study the existence of minimal supersolutions of BSDEs under a family of mutually singular probability measures. We consider generators that are jointly lower semicontinuous, positive, and either convex in the control variable and monotone in the value variable, or that fulfill a specific normalization property.