A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions

TL;DR

This paper studies backward stochastic partial differential equations with singular terminal conditions, establishing their well-posedness and regularity, motivated by non-Markovian portfolio liquidation models.

Contribution

It introduces new existence, uniqueness, and regularity results for a class of backward SPDEs with singular terminal conditions, relevant to non-Markovian control problems.

Findings

Proves existence and uniqueness of solutions

Establishes regularity properties of solutions

Applies results to portfolio liquidation models

Abstract

We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is pre-specified. The analysis of such control problems is motivated by models of optimal portfolio liquidation.