Results 1 to 10 of about 39,858 (272)
A Class of Pursuit Problems in 3D Space via Noncooperative Stochastic Differential Games
AerospaceThis paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic ...
Yu Bai, Di Zhou, Zhen He
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Approximate solutions of continuous-time stochastic games [PDF]
, 2016 The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a model game.
Averboukh, Yurii
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Journal of Differential Equations, 1972 Consider a stochastic differential system of \(m\) equations \[ d\xi(t)=f(t,\xi(t), y_1,\ldots, y_N)\,dt+ \sigma(t, \xi(t))\,dw(t),\quad \xi(s) =x_0, \] where the player \(y_i\) chooses a control function with values in a control set \(Y_i\). Denote by \(\tau\) the exit time of \(\xi(t)\) from a cylinder \(\{s
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Differential games for stochastic partial differential equations [PDF]
Nagoya Mathematical Journal, 1993 In this paper we are concerned with zero-sum two-player finite horizon games for stochastic partial differential equations (SPDE in short). The main aim is to formulate the principle of dynamic programming for the upper (or lower) value function and investigate the relationship between upper (or lower) value function and viscocity solution of min-max ...
Fleming, W. H., Nisio, M.
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Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls
MathematicsIn this paper, a two-player nonzero-sum stochastic differential game problem is studied with both players using switching controls. A verification theorem associated with a set of variational inequalities is established as a sufficient criterion for Nash
Yongxin Liu, Hui Min
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Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications [PDF]
, 2010 The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the ...
Bensoussan +22 more
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MathematicsWe establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional
Wanyang Dai
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, 2014 This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition.
Hamadène, Said, Mu, Rui
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A stochastic differential reinsurance game [PDF]
Journal of Applied Probability, 2010 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.
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On the adjoint Markov policies in stochastic differential games [PDF]
, 2019 We consider time-homogeneous uniformly nondegenerate stochastic differential games in domains and propose constructing $\varepsilon$-optimal strategies and policies by using adjoint Markov strategies and adjoint Markov policies which are actually time ...
Krylov, N. V.
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