We consider a callable convertible bond in a setting where the bondholder (and firm) face liquidity issues which are modelled by constraning the agents so that they can only act at the event times of a Poisson process. This is then an example of a constrained Dynkin game. We show how to solve the problem (typically by reducing to a Poisson optimal stopping problem for one or other agent.) We also discuss how to model the Poisson constraint, and the extent to which the choice of formulation affects the solution.

Joint work with Gechun Liang and Edward Wang.