# Dynkin Games with Poisson Random Intervention Times

@article{Liang2019DynkinGW, title={Dynkin Games with Poisson Random Intervention Times}, author={Gechun Liang and Haodong Sun}, journal={SIAM J. Control. Optim.}, year={2019}, volume={57}, pages={2962-2991} }

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.

## Figures, Tables, and Topics from this paper

## 2 Citations

Risk-sensitive Dynkin games with heterogeneous Poisson random intervention times.

- Mathematics
- 2020

The paper solves constrained Dynkin games with risk-sensitive criteria, where two players are allowed to stop at two independent Poisson random intervention times, via the theory of backward…

Callable convertible bonds under liquidity constraints

- Economics, Mathematics
- 2021

Abstract. This paper provides a complete solution to the callable convertible bond studied in [Liang and Sun, Dynkin games with Poisson random intervention times, SIAM Journal on Control and…

## References

SHOWING 1-10 OF 42 REFERENCES

Optimal Switching at Poisson Random Intervention Times

- Computer Science, Mathematics
- 2013

This paper introduces a new class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is…

The Continuous Time Nonzero-Sum Dynkin Game Problem and Application in Game Options

- Computer Science, MathematicsSIAM J. Control. Optim.
- 2010

The nonzero-sum Dynkin game in continuous time, which is a two-player noncooperative game on stopping times, is studied and it is shown that it has a Nash equilibrium point for general stochastic processes.

Dynkin Game of Convertible Bonds and Their Optimal Strategy

- Economics, Mathematics
- 2015

This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality…

Dynkin games and martingale methods

- Mathematics
- 1984

We consider non-Markov stochastic games with stopping times, so-called Dynkin games. Using the martingale point of view, we show the existence of a saddle-point under general assumptions

On the Robust Dynkin Game

- Mathematics
- 2015

We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (Let us denote the value by…

Stopping games with randomized strategies

- Mathematics
- 2001

Abstract. We study stopping games in the setup of Neveu. We prove the existence of a uniform value (in a sense defined below), by allowing the players to use randomized strategies. In constrast with…

On a randomized strategy in Neveu's stopping problem

- Mathematics
- 1985

In Neveu's variant of the stopping problem, a randomized strategy is considered in order to relax a condition on values of two stochastic sequences. We shall describe the variant of the problem as a…

Nash equilibria of threshold type for two-player nonzero-sum games of stopping

- Mathematics
- 2015

This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not non-singular boundary behaviour (in the sense of It\^o and McKean (1974), p.\…

The Value of Zero-Sum Stopping Games in Continuous Time

- Mathematics, Computer ScienceSIAM J. Control. Optim.
- 2005

It is proved that the value in randomized stopping times exists as soon as the payoff processes are right-continuous, as opposed to existing literature, which does not assume any conditions on the relations between the payoff process.

Backward stochastic differential equations with reflection and Dynkin games

- Mathematics
- 1996

We establish existence and uniqueness results for adapted solutions of backward stochastic differential equations (BSDE's) with two reflecting barriers, generalizing the work of El Karoui,…