Recursive Optimal Stopping with Poisson Stopping Constraints

TL;DR

This paper addresses a recursive optimal stopping problem constrained by Poisson intervention times, employing PBSDE with jumps and a decomposition method to solve and analyze the problem, with applications to American option pricing.

Contribution

It introduces a novel decomposition approach for recursive stopping problems with Poisson constraints and applies BSDE comparison theorems for value function representation.

Findings

Decomposition method effectively separates the problem into sub-problems.

Representation of the value function using BSDE comparison theorem.

Application to American option pricing under Poisson constraints.

Abstract

This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random intervention times, and jumps play a significant role not only through the stopping times but also in the recursive objective functional and model coefficients. To solve the problem, we propose a decomposition method based on Jacod-Pham that allows us to separate the problem into a series of sub-problems between each pair of consecutive Poisson stopping times. To represent the value function of the recursive optimal stopping problem when the initial time falls between two consecutive Poisson stopping times and the generator is concave/convex, we leverage the comparison theorem of BSDEs with jumps. We then apply the representation result to American option pricing in a nonlinear market with Poisson stopping constraints.