×

Error estimates for stochastic differential games: the adverse stopping case. (English) Zbl 1130.91014

The authors consider a 2-player zero-sum stochastic differential game. Player 1 has a set of controls and wishes to minimize the gain \(u\); player 2, may stop the game and wishes to maximize \(u\). This paper gives lower and upper bound error estimates for solving the resulting non-convex Isaacs equation. The upper bound relies on a Krylov regularization [N. V. Krylov, St. Petersbg. Math. J. 9, No. 3, 639–650 (1998) and Algebra Anal. 9, No. 3, 245–256 (1997; Zbl 0902.65035); Probab. Theory Relat. Fields 117, No. 1, 1–16 (2000; Zbl 0971.65081)].

MSC:

91A23 Differential games (aspects of game theory)
91A15 Stochastic games, stochastic differential games
PDFBibTeX XMLCite
Full Text: DOI Link