Dynkin games with Poisson random intervention times

TL;DR

This paper studies a new class of Dynkin games where players can only stop at Poisson arrival times, characterizing the value function via backward stochastic differential equations and applying it to convertible bonds.

Contribution

It introduces a novel Dynkin game framework with Poisson intervention times and characterizes the value function using backward stochastic differential equations.

Findings

Characterization of the value function via backward stochastic differential equations.

Application to optimal conversion and calling strategies of convertible bonds.

Asymptotic analysis as Poisson intensity increases.

Abstract

This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The paper further applies the model to study the optimal conversion and calling strategies of convertible bonds, and their asymptotics when the Poisson intensity goes to infinity.