A Dynkin game with asymmetric information

Abstract

We study a Dynkin game with asymmetric information. The game has a random expiry time, which is exponentially distributed and independent of the underlying process. The players have asymmetric information on the expiry time, namely only one of the players is able to observe its occurrence. We propose a set of conditions under which we solve the saddle point equilibrium and study the implications of the information asymmetry. Results are illustrated with an explicit example.

Keywords:

• Dynkin game
• Nash equilibrium
• Israeli option
• default risk
• linear diffusion
• resolvent operator

2000 Mathematics Subject Classification::

• 60G40
• 60J60

Acknowledgements

The authors thank Prof. Fred Espen Benth for helpful discussions. Authors would also like to thank the anonymous referees for their constructive comments on earlier version of this study.

Notes

^1. [email protected]

Additional information

Notes on contributors

Jukka Lempa

1 1. [email protected]