Second order BSDE under monotonicity condition and liquidation problem under uncertainty *

TL;DR

This paper studies an optimal closure problem under Knightian uncertainty using second order backward stochastic differential equations with monotone generators, deriving the value function and optimal control.

Contribution

It introduces a novel approach to solve the liquidation problem under uncertainty via second order BSDEs with singular terminal conditions.

Findings

Derived the value function for the liquidation problem.

Established existence of minimal super-solutions to the second order BSDE.

Provided a characterization of the optimal control strategy.

Abstract

In this work we investigate an optimal closure problem under Knightian uncertainty. We obtain the value function and an optimal control as the minimal (super-)solution of a second order BSDE with monotone generator and with a singular terminal condition.