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

In this paper we study the nonzero-sum Dynkin game in continuous time, which is a two-player noncooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach.

[1]  J. Bismut.  Sur un problème de dynkin , 1977 .

[2]  Yuri Kifer,et al.  Game options , 2000, Finance Stochastics.

[3]  Hiroaki Morimoto,et al.  Non-zero-sum discrete parameter stochastic games with stopping times , 1986 .

[4]  Christoph Kühn,et al.  Game contingent claims in complete and incomplete markets. , 2004 .

[5]  Avner Friedman,et al.  Nonzero-sum stochastic differential games with stopping times and free boundary problems , 1977 .

[6]  Patrick Cattiaux,et al.  Existence of a quasi-markov nash equilibrium for non-zero sum markov stopping games , 1990 .

[7]  J. Lepeltier,et al.  Le jeu de dynkin en theorie generale sans l'hypothese de mokobodski , 1984 .

[8]  Erik Ekstrom,et al.  On the value of optimal stopping games , 2006 .

[9]  Rida Laraki,et al.  The Value of Zero-Sum Stopping Games in Continuous Time , 2005, SIAM J. Control. Optim..

[10]  E. B. Dynkin,et al.  Game variant of a problem on optimal stopping , 1969 .

[11]  Said Hamadène,et al.  Mixed Zero-Sum Stochastic Differential Game and American Game Options , 2006, SIAM J. Control. Optim..

[12]  N. Karoui.  Les Aspects Probabilistes Du Controle Stochastique , 1981 .

[13]  C. SIAMJ..  CONTINUOUS-TIME DYNKIN GAMES WITH MIXED STRATEGIES , 2002 .

[14]  Goran Peskir,et al.  Optimal Stopping Games for Markov Processes , 2008, SIAM J. Control. Optim..

[15]  W. Schachermayer,et al.  Pricing Derivatives of American and Game Type in Incomplete Markets , 2003 .

[16]  A. Kyprianou,et al.  Further calculations for Israeli options , 2004 .

[17]  Ł. Stettner.  Zero-sum Markov games with stopping and impulsive strategies , 1982 .

[18]  P. Meyer,et al.  Probabilités et potentiel , 1966 .

[19]  H. Morimoto.  Dynkin games and martingale methods , 1984 .

[20]  A. Bensoussan,et al.  Nonlinear variational inequalities and differential games with stopping times , 1974 .

[21]  Luis H. R. Alvarez,et al.  A Class of Solvable Stopping Games , 2008 .

[22]  Hideo Nagai,et al.  Non zero-sum stopping games of symmetric Markov processes , 1987 .

[23]  Yoshio Ohtsubo,et al.  A Nonzero-Sum Extension of Dynkin's Stopping Problem , 1987, Math. Oper. Res..