A System of BSDEs with Singular Terminal Values Arising in Optimal Liquidation with Regime Switching

TL;DR

This paper introduces a novel system of backward stochastic differential equations with jumps and singular terminal values to solve an optimal liquidation problem involving regime switching, dark pools, and multiple regimes, providing existence and uniqueness results.

Contribution

It is the first to analyze a system of BSDEs with jumps and singular terminal values in the context of regime switching, solving the associated stochastic control problem.

Findings

Established existence of solutions for the new BSDE system.

Proved uniqueness of the solutions, ensuring well-posedness.

Applied the results to optimal liquidation with regime switching.

Abstract

We study a stochastic control problem with regime switching arising in an optimal liquidation problem with dark pools and multiple regimes. The new feature of this model is that it introduces a system of BSDEs with jumps and with singular terminal values, which appears in literature for the first time. The existence result for this system is obtained. As a result, we solve the stochastic control problem with regime switching. More importantly, the uniqueness result of this system is also obtained, in contrast to merely minimal solutions established in most related literature.