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| Content Provider | Springer Nature Link |
|---|---|
| Author | Buckdahn, Rainer Li, Juan |
| Copyright Year | 2011 |
| Abstract | 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. |
| Ending Page | 678 |
| Page Count | 32 |
| Starting Page | 647 |
| File Format | |
| ISSN | 01689673 |
| e-ISSN | 16183932 |
| Journal | Acta Mathematicae Applicatae Sinica |
| Issue Number | 4 |
| Volume Number | 27 |
| Language | English |
| Publisher | Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |
| Publisher Date | 2011-09-09 |
| Publisher Place | Heildeberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | reflected backward stochastic differential equations viscosity solution dynamic programming principle Isaacs equations with obstacles Theoretical, Mathematical and Computational Physics Stochastic ordinary differential equations value function stochastic differential games Dynamic programming Applications of Mathematics Math Applications in Computer Science |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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