-
Previous Article
Stability of solitary-wave solutions to the Hirota-Satsuma equation
- DCDS Home
- This Issue
-
Next Article
On a $\nu$-continuous family of strong solutions to the Euler or Navier-Stokes equations with the Navier-Type boundary condition
Systems of Bellman equations to stochastic differential games with non-compact coupling
| 1. | School of Management, International Center for Decision and Risk Analysis, University of Texas at Dallas, 800 W. Campbell Rd, SM30, Richardson, TX 75080-3021, United States |
| 2. | Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, NRW, 53115 Bonn, Germany |
| 3. | Harvard Mathematics Department, One Oxford Street, Cambridge, MA 02138, United States |
-div$(a(x)\nabla u_{\nu}) +\lambda u_{\nu}=H_{\nu}(x, Du) \, $
with applications for the solution of stochastic differential games with $N$ players, where $N$ is an arbitrary but positive number. The Hamiltonian $H$ of the non-linear system satisfies a quadratic growth condition in $D u$ and contains interactions between the players in the form of non-compact coupling terms $\nabla u_{i} \cdot\nabla u_j$. A $L^{\infty}\cap H^1$-estimate and regularity results are shown, mainly in two-dimensional space. The coupling arises from cyclic non-market interaction of the control variables.
| [1] |
Jingzhen Liu, Ka-Fai Cedric Yiu. Optimal stochastic differential games with VaR constraints. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1889-1907. doi: 10.3934/dcdsb.2013.18.1889 |
| [2] |
Alain Bensoussan, Jens Frehse, Christine Grün. Stochastic differential games with a varying number of players. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1719-1736. doi: 10.3934/cpaa.2014.13.1719 |
| [3] |
Tyrone E. Duncan. Some linear-quadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions. Discrete & Continuous Dynamical Systems, 2015, 35 (11) : 5435-5445. doi: 10.3934/dcds.2015.35.5435 |
| [4] |
Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos. Nonzero-sum stochastic differential games with additive structure and average payoffs. Journal of Dynamics & Games, 2014, 1 (4) : 555-578. doi: 10.3934/jdg.2014.1.555 |
| [5] |
Beatris Adriana Escobedo-Trujillo, Alejandro Alaffita-Hernández, Raquiel López-Martínez. Constrained stochastic differential games with additive structure: Average and discount payoffs. Journal of Dynamics & Games, 2018, 5 (2) : 109-141. doi: 10.3934/jdg.2018008 |
| [6] |
Qingmeng Wei, Zhiyong Yu. Time-inconsistent recursive zero-sum stochastic differential games. Mathematical Control & Related Fields, 2018, 8 (3&4) : 1051-1079. doi: 10.3934/mcrf.2018045 |
| [7] |
Beatris A. Escobedo-Trujillo. Discount-sensitive equilibria in zero-sum stochastic differential games. Journal of Dynamics & Games, 2016, 3 (1) : 25-50. doi: 10.3934/jdg.2016002 |
| [8] |
Xiangxiang Huang, Xianping Guo, Jianping Peng. A probability criterion for zero-sum stochastic games. Journal of Dynamics & Games, 2017, 4 (4) : 369-383. doi: 10.3934/jdg.2017020 |
| [9] |
Mathias Staudigl, Srinivas Arigapudi, William H. Sandholm. Large deviations and Stochastic stability in Population Games. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021021 |
| [10] |
Samuel Drapeau, Peng Luo, Alexander Schied, Dewen Xiong. An FBSDE approach to market impact games with stochastic parameters. Probability, Uncertainty and Quantitative Risk, 2021, 6 (3) : 237-260. doi: 10.3934/puqr.2021012 |
| [11] |
Tyrone E. Duncan. Some partially observed multi-agent linear exponential quadratic stochastic differential games. Evolution Equations & Control Theory, 2018, 7 (4) : 587-597. doi: 10.3934/eect.2018028 |
| [12] |
Rui Mu, Zhen Wu. Nash equilibrium points of recursive nonzero-sum stochastic differential games with unbounded coefficients and related multiple\\ dimensional BSDEs. Mathematical Control & Related Fields, 2017, 7 (2) : 289-304. doi: 10.3934/mcrf.2017010 |
| [13] |
Jun Moon. Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021026 |
| [14] |
Libin Mou, Jiongmin Yong. Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method. Journal of Industrial & Management Optimization, 2006, 2 (1) : 95-117. doi: 10.3934/jimo.2006.2.95 |
| [15] |
Alejandra Fonseca-Morales, Onésimo Hernández-Lerma. A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models†. Journal of Dynamics & Games, 2017, 4 (3) : 195-203. doi: 10.3934/jdg.2017012 |
| [16] |
Dejian Chang, Zhen Wu. Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance. Journal of Industrial & Management Optimization, 2015, 11 (1) : 27-40. doi: 10.3934/jimo.2015.11.27 |
| [17] |
Cyril Imbert, Sylvia Serfaty. Repeated games for non-linear parabolic integro-differential equations and integral curvature flows. Discrete & Continuous Dynamical Systems, 2011, 29 (4) : 1517-1552. doi: 10.3934/dcds.2011.29.1517 |
| [18] |
Lin Xu, Rongming Wang, Dingjun Yao. Optimal stochastic investment games under Markov regime switching market. Journal of Industrial & Management Optimization, 2014, 10 (3) : 795-815. doi: 10.3934/jimo.2014.10.795 |
| [19] |
Sylvain Sorin, Guillaume Vigeral. Reversibility and oscillations in zero-sum discounted stochastic games. Journal of Dynamics & Games, 2015, 2 (1) : 103-115. doi: 10.3934/jdg.2015.2.103 |
| [20] |
Antoine Hochart. An accretive operator approach to ergodic zero-sum stochastic games. Journal of Dynamics & Games, 2019, 6 (1) : 27-51. doi: 10.3934/jdg.2019003 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]