Computation of nash equilibrium pairs of a stochastic differential game

2007 ◽  
Vol 2 (3) ◽  
pp. 225-238 ◽  
Author(s):  
Y. Yavin ◽  
G. Reuter
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Stochastic Differential Game

scholarly journals A stochastic differential reinsurance game

2010 ◽  
Vol 47 (2) ◽  
pp. 335-349 ◽  
Author(s):  
Xudong Zeng
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Payoff Function ◽  
The Other ◽  
Insurance Companies ◽  
Stochastic Differential Game ◽  
Claim Size ◽  
Expected Payoff ◽  
Exit Probability ◽  
Risk Of Exposure

We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single payoff function which depends on the surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize this expected payoff, while the other company simultaneously chooses a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of this stochastic differential game and solve it explicitly for the case of maximizing/minimizing the exit probability.

scholarly journals A stochastic differential reinsurance game

2010 ◽  
Vol 47 (02) ◽  
pp. 335-349 ◽  
Author(s):  
Xudong Zeng
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Payoff Function ◽  
The Other ◽  
Insurance Companies ◽  
Stochastic Differential Game ◽  
Claim Size ◽  
Expected Payoff ◽  
Exit Probability ◽  
Risk Of Exposure

We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single payoff function which depends on the surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize this expected payoff, while the other company simultaneously chooses a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of this stochastic differential game and solve it explicitly for the case of maximizing/minimizing the exit probability.

scholarly journals Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 132
Author(s):  
Valery Y. Glizer
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Cheap Control ◽  
Optimal Values ◽  
Definition Of ◽  
Zero Sum ◽  
Equilibrium Sequence

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

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