caa a22 4500 445830824 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10255-011-0068-8 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0068-8 Stochastic differential games with reflection and related obstacle problems for Isaacs equations [Elektronische Daten] [Rainer Buckdahn, Juan Li] In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bellman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of El Karoui, Kapoudjian, Pardoux, Peng and Quenez (1997), which turns out to be very useful because it allows us to estimate the L p -distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 stochastic differential games nationallicence value function nationallicence reflected backward stochastic differential equations nationallicence dynamic programming principle nationallicence Isaacs equations with obstacles nationallicence viscosity solution nationallicence Buckdahn Rainer Département de Mathématiques, Université de Bretagne Occidentale, 6, avenue Victor-le-Gorgeu, B.P. 809, 29285, Brest cedex, France aut Li Juan School of Mathematics and Statistics, Shandong University at Weihai, 264209, Weihai, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/4(2011-10-01), 647-678 0168-9673 27:4<647 2011 27 10255 https://doi.org/10.1007/s10255-011-0068-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0068-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Buckdahn Rainer Département de Mathématiques, Université de Bretagne Occidentale, 6, avenue Victor-le-Gorgeu, B.P. 809, 29285, Brest cedex, France aut NATIONALLICENCE 700 1- Li Juan School of Mathematics and Statistics, Shandong University at Weihai, 264209, Weihai, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/4(2011-10-01), 647-678 0168-9673 27:4<647 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer