Optimal stopping games for Markov processes

SIAM Journal on Control and Optimization

Volumn 47, Issue 2, 2008, Pages 684-702

  Ekström, Erik ^a   Peskir, Goran ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Markov process; Martingale; Nash equilibrium; Optimal stopping; Optimal stopping game; Saddle point; Snell envelope; Stackelberg equilibrium

Indexed keywords

MARKOV PROCESSES; PROBABILITY DENSITY FUNCTION; TELECOMMUNICATION NETWORKS;

MARTINGALE; NASH EQUILIBRIUM; OPTIMAL STOPPING; OPTIMAL STOPPING GAME; SADDLE POINT; SNELL ENVELOPE; STACKELBERG EQUILIBRIUM;

GAME THEORY;

EID: 55549118591     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060673916     Document Type: Article

References (23)

1. E. J. BAURDOUX AND A. E. KYPRIANOU, Further calculations for Israeli options, Stoch. Stoch. Rep., 76 (2004), pp. 549-569.
2. A. BENSOUSSAN AND A. FRIEDMAN, Nonlinear variational inequalities and differential games with stopping times, J. Funct. Anal., 16 (1974), pp. 305-352.
3. A. BENSOUSSAN AND A. FRIEDMAN, Nonzero-sum stochastic differential games with stopping times and free boundary problems, Trans. Amer. Math. Soc., 231 (1977), pp. 275-327.
4. F. BOETIUS, Bounded variation singular stochastic control and Dynkin game, SIAM J. Control Optim., 44 (2005), pp. 1289-1321.
5. E. B. DYNKIN, Game variant of a problem of optimal stopping, Soviet Math. Dokl., 10 (1969), pp. 16-19.
6. E. EKSTRöm, Properties of game options, Math. Methods Oper. Res., 63 (2006), pp. 221-238.
7. E. EKSTRöm AND S. VILLENEUVE, On the value of optimal stopping games, Ann. Appl. Probab., 16 (2006), pp. 1576-1596.
8. N. V. ELBAKIDZE, Construction of the cost and optimal policies in a game problem of stopping a Markov process, Theory Probab. Appl., 21 (1976), pp. 163-168.
9. E. B. FRID, The optimal stopping rule for a two-person Markov chain with opposing interests, Theory Probab. Appl., 14 (1969), pp. 713-716.
10. A. FRIEDMAN, Stochastic games and variational inequalities, Arch. Ration. Mech. Anal., 51 (1973), pp. 321-346.
11. P. V. GAPEEV, The Spread Option Optimal Stopping Game, Exotic Option Pricing and Advanced Lévy Models, John Wiley, New York, 2005, pp. 293-305.
12. S. M. GUSEIN-ZADE, On a game connected with a Wiener process, Theory Probab. Appl., 14 (1969), pp. 701-704.
13. Y. KIFER, Optimal stopping in games with continuous time, Theory Probab. Appl., 16 (1971), pp. 545-550.
14. Y. KIFER, Game options, Finance Stoch., 4 (2000), pp. 443-463.
15. C. KÜHN AND A. E. KYPRIANOU, Callable puts as composite exotic options, Math. Finance, 17 (2007), pp. 487-502.
16. A. E. KYPRIANOU, Some calculations for Israeli options, Finance Stoch., 8 (2004), pp. 73-86.
17. R. LARAKI AND E. SOLAN, The value of zero-sum stopping games in continuous time, SIAM J. Control Optim., 43 (2005), pp. 1913-1922.
18. J. P. LEPELTIER AND M. A. MAINGUENEAU, Le jeu de Dynkin en théorie générale sans l'hypothèse de Mokobodski, Stochastics, 13 (1984), pp. 25-44.
19. G. PESKIR AND A. N. SHIRYAEV, Optimal Stopping and Free-Boundary Problems, Lectures Math. ETH Zürich, Birkhäuser, Basel, 2006.
20. A. N. SHIRYAEV, Optimal Stopping Rules, Springer-Verlag, Berlin, 1978.
21. J. L. SNELL, Applications of martingale system theorems, Trans. Amer. Math. Soc., 73 (1952), pp. 293-312.
22. L. STETTNER, Zero-sum Markov games with stopping and impulsive strategies, Appl. Math. Optim., 9 (1982), pp. 1-24.
23. L. STETTNER, On closedness of general zero-sum stopping game, Bull. Poli. Acad. Sci. Math., 32 (1984), pp. 351-361.