Malliavin derivative and sensitivity for optimal liquidation

TL;DR

This paper establishes the existence and properties of the Malliavin derivative for solutions of certain backward stochastic differential equations with terminal singularities, and applies these results to optimal liquidation sensitivity analysis.

Contribution

It introduces a novel analysis of the Malliavin derivative for BSDEs with terminal singularities and explores its implications for PDE regularity and liquidation sensitivity.

Findings

Malliavin derivative exists for solutions with terminal singularity

Asymptotic behavior of the derivative near terminal time characterized

Application to sensitivity analysis in liquidation problems

Abstract

We prove that the solution of the backward stochastic differential equation with terminal singularity has a Malliavin derivative, which is the limit of the derivative of the approximating sequence. We also provide the asymptotic behavior of this derivative close to the terminal time. We apply this result to the regularity of the related partial differential equation and to the sensitivity of the liquidation problem.