Results 231 to 240 of about 39,851 (271)

Stochastic differential game in high frequency market

Automatica, 2018
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Saito, Taiga, Takahashi, Akihiko
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Stochastic Differential Games

2014
In this chapter, we will deal with zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games, via the dynamic programming principle.In Sect. 4.1, we are concerned with basic concepts and definitions and we introduce stochastic differential games, referring to (Controlled ...
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Zero-Sum Risk-Sensitive Stochastic Differential Games

Mathematics of Operations Research, 2012
We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton–Jacobi–Isaacs equations.
Basu, Arnab, Ghosh, Mrinal K
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An approach-evasion differential game: Stochastic guide

Proceedings of the Steklov Institute of Mathematics, 2010
The differential equation \[ \dot{x}=f(t,x,u,v), t_{0}\leq t\leq \vartheta, u\in P, v\in Q, \] is approached by a positional differential game. The time \(\vartheta\) of the motion \(x[t],t_{0}\leq t\leq \vartheta\) belongs to a set \(M\) inside a set N and the evasion up to the time \(\vartheta\) of the motion \(x[t],t_{0}\leq t\leq \vartheta ...
Krasovskii, N. N., Kotel'nikova, A. N.
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Stochastic zero-sum differential games and backward stochastic differential equations

Random Operators and Stochastic Equations, 2023
Abstract In this paper, we study the stochastic zero-sum differential game in finite horizon in a general case. We first prove that the BSDE associated with a specific generator (the Hamiltonian function for the game) has a unique solution.
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Stochastic Differential Mean Field Games

2018
The goal of this chapter is to propose solutions to asymptotic forms of the search for Nash equilibria for large stochastic differential games with mean field interactions. We implement the Mean Field Game strategy, initially developed by Lasry and Lions in an analytic set-up, in a purely probabilistic framework.
René Carmona, François Delarue
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Risk-Sensitive Mean-Field Stochastic Differential Games

IFAC Proceedings Volumes, 2011
In this paper, we study a class of risk-sensitive mean-field stochastic di fferential games. Under regularity assumptions, we use results from standard risk-sensitive di fferential game theory to show that the mean- field value of the exponentiated cost functional coincides with the value function of a Hamilton-Jacobi-Bellman-Fleming (HJBF) equation ...
Tembine, Hamidou, Zhu, Quanyan, Basar, Tamer   +2 more
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Deterministic and Stochastic Differential Games

2016
This chapter introduces the theory of deterministic and stochastic differential games, including the dynamic optimization techniques, (stochastic) differential games and their solution concepts, which will lay a foundation for later study.
Cheng-ke Zhang, Huai-nian Zhu, Hai-ying Zhou, Ning Bin   +3 more
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On a problem of stochastic differential games

Journal of Optimization Theory and Applications, 1976
The process of bargaining between management and union during a strike is modelled by a nonlinear stochastic differential game. It is assumed that the two sides bargain in the mood of a cooperative game. A pair of Pareto-optimal strategies is obtained.
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Adaptive Stabilization of Noncooperative Stochastic Differential Games

SIAM Journal on Control and Optimization
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Nian Liu, Lei Guo
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