Optimal stopping and stochastic control differential games for jump diffusions

Baghéry, Fouzia; Haadem, Sven; Øksendal, Bernt; Turpin, Isabelle

doi:10.1080/17442508.2011.652116

Cited by 5 publications

(10 citation statements)

References 7 publications

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“…The authors presented Nash equilibria, rather than saddle pairs, of strategies [10]. Moreover, the papers [11][12][13][14][15][16][17] considered a zero-sum stochastic differential game between controller and stopper, where one player (controller) chooses a control process (⋅) and the other (stopper) chooses a stopping . One player tries to maximize the reward and the other to minimize it.…”

Section: Abstract and Applied Analysismentioning

confidence: 99%

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Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions

Wang

Song

Zheng

et al. 2013

Abstract and Applied Analysis

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We consider a nonzero-sum stochastic differential game which involves two players, a controller and a stopper. The controller chooses a control process, and the stopper selects the stopping rule which halts the game. This game is studied in a jump diffusions setting within Markov control limit. By a dynamic programming approach, we give a verification theorem in terms of variational inequality-Hamilton-Jacobi-Bellman (VIHJB) equations for the solutions of the game. Furthermore, we apply the verification theorem to characterize Nash equilibrium of the game in a specific example.

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Section: Abstract and Applied Analysismentioning

confidence: 99%

“…In [3], the authors studied the stochastic differential games between two controllers. The work in [17] was carried out for a zero-sum stochastic differential game between a controller and a stopper.…”

Section: Abstract and Applied Analysismentioning

confidence: 99%

Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions

Wang

Song

Zheng

et al. 2013

Abstract and Applied Analysis

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“…Our setup and approach is related to [7,8,9,10]. In [7], the classic verification theorem of VIHJB equations obtained by Dynkin's formula gives a solution for combined optimal stopping and stochastic control problem in strong formulation.…”

Section: Introductionmentioning

confidence: 99%

“…In [7], the classic verification theorem of VIHJB equations obtained by Dynkin's formula gives a solution for combined optimal stopping and stochastic control problem in strong formulation. Later, [8,9,10] applied the verification theorem to solve different stochastic control problems and stochastic differential games for jump diffusions. However, the agent problem that we consider is in weak formulation, in the sense that the agent chooses a probability measure under which the state process evolves.…”

Section: Introductionmentioning

confidence: 99%

Optimal Quitting in a Dynamic Agency Problem for Jump Diffusions

Wang¹

2013

J. Inf. Comput. Sci.

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In this paper, we study the agent's optimal quitting in a continuous-time principal-agent problem, where the agent is payed once at the end of the contract. In a jump diffusion setting, we formulate the agency problem as a combined optimal stopping and stochastic control problem in weak formulation. To find the solutions, we develop the classical verification theorem in terms of Variational Inequality Hamilton-Jacobi-Bellman (VIHJB) equations in weak formulation. Finally, we solve explicitly the VIHJB equations in a special case.

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“…Problems that combine discretionary stopping and stochastic optimal control have attracted much attention over recent years; in particular there is a significant amount of literature on models of this kind in which a single controller uses continuous controls to modify the system dynamics (see for example [4,2,5]). Game-theoretic formulations of the problem in which the task of controlling the system dynamics and exit time is divided between two players who act according to separated interests have also been studied [1].…”

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confidence: 99%

A Viscosity Approach to Stochastic Differential Games of Control and Stopping Involving Impulsive Control

Mguni

2018

Preprint

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This paper analyses a stochastic differential game of control and stopping in which one of the players modifies a diffusion process using impulse controls, an adversary then chooses a stopping time to end the game. The paper firstly establishes the regularity and boundedness of the upper and lower value functions from which an appropriate variant of the dynamic programming principle (DPP) is derived. It is then proven that the upper and lower value functions coincide so that the game admits a value and that the value of the game is a unique viscosity solution to a HJBI equation described by a double obstacle quasi-integro-variational inequality.

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Optimal stopping and stochastic control differential games for jump diffusions

Cited by 5 publications

References 7 publications

Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions

Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions

Optimal Quitting in a Dynamic Agency Problem for Jump Diffusions

A Viscosity Approach to Stochastic Differential Games of Control and Stopping Involving Impulsive Control

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