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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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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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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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International Journal of Robust and Nonlinear Control, 2019
In this paper, we consider risk‐sensitive optimal control and differential games for stochastic differential delayed equations driven by Brownian motion. The problems are related to robust stochastic optimization with delay due to the inherent feature of
Jun Moon
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In this paper, we consider risk‐sensitive optimal control and differential games for stochastic differential delayed equations driven by Brownian motion. The problems are related to robust stochastic optimization with delay due to the inherent feature of
Jun Moon
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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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Stochastic zero-sum differential games and backward stochastic differential equations
Random Operators and Stochastic Equations, 2023Abstract 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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Nonzero-sum risk-sensitive stochastic differential games with discounted costs
, 2020We study nonzero-sum stochastic differential games with risk-sensitive discounted cost criteria. Under fairly general conditions on drift term and diffusion coefficients, we establish a Nash equilibrium in Markov strategies for the discounted cost ...
M. K. Ghosh +3 more
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Ergodic risk-sensitive stochastic differential games with reflecting diffusions in a bounded domain
, 2020In this article, we study risk-sensitive stochastic differential games for controlled reflecting diffusion processes in a smooth bounded domain. We analyze the ergodic cost evaluation criterion for both nonzero-sum games and zero-sum games.
M. K. Ghosh, Somnath Pradhan
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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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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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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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