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Stochastic differential game in high frequency market
Automatica, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saito, Taiga, Takahashi, Akihiko
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Zero-Sum Risk-Sensitive Stochastic Differential Games
Mathematics of Operations Research, 2012We 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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Stochastic Differential Mean Field Games
2018The 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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An approach-evasion differential game: Stochastic guide
Proceedings of the Steklov Institute of Mathematics, 2010The 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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Modeling forest carbon sink trading with carbon credit using stochastic differential game
Environmental science and pollution research international, 2023Jingxiu Song, D. Wu
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Asian journal of control, 2018
In this paper, we deal with a new kind of partially observed nonzero‐sum differential game governed by stochastic differential delay equations. One of the special features is that the controlled system and the utility functionals involve both delays in ...
Bixuan Yang, T. Guo, Jinbiao Wu
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In this paper, we deal with a new kind of partially observed nonzero‐sum differential game governed by stochastic differential delay equations. One of the special features is that the controlled system and the utility functionals involve both delays in ...
Bixuan Yang, T. Guo, Jinbiao Wu
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Deterministic and Stochastic Differential Games
2016This 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 +3 more
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Risk-Sensitive Mean-Field Stochastic Differential Games
IFAC Proceedings Volumes, 2011In 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 +2 more
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Optimal control applications & methods, 2019
We study a class of coupled nonlinear matrix differential equations arising in connection with the solution of a zero‐sum two‐player linear quadratic (LQ) differential game for a dynamical system modeled by an Itô differential equation subject to random ...
V. Dragan, S. Aberkane, T. Morozan
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We study a class of coupled nonlinear matrix differential equations arising in connection with the solution of a zero‐sum two‐player linear quadratic (LQ) differential game for a dynamical system modeled by an Itô differential equation subject to random ...
V. Dragan, S. Aberkane, T. Morozan
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On a problem of stochastic differential games
Journal of Optimization Theory and Applications, 1976The 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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