Density analysis of non-Markovian BSDEs and applications to biology and finance

TL;DR

This paper establishes conditions for the Malliavin differentiability of solutions to non-Markovian BSDEs and explores their density properties, with applications in biology and finance.

Contribution

It provides new conditions ensuring the existence of densities for solutions to path-dependent stochastic Lipschitz BSDEs, extending previous results.

Findings

Solutions are Malliavin differentiable under certain conditions

Density existence results for first components of BSDE solutions

Applications demonstrated in gene expression and financial pricing

Abstract

In this paper, we provide conditions which ensure that stochastic Lipschitz BSDEs admit Malliavin differentiable solutions. We investigate the problem of existence of densities for the first components of solutions to general path-dependent stochastic Lipschitz BSDEs and obtain results for the second components in particular cases. We apply these results to both the study of a gene expression model in biology and to the classical pricing problems in mathematical finance.