Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach

Pamen, Olivier Menoukeu

doi:10.1007/s10957-013-0484-4

Cited by 33 publications

(26 citation statements)

References 35 publications

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“…That is to say, condition (19) together with the PDEs system (20) guarantees that the reduction of PDE (12) from an infinite dimensional one to its finite dimensional counterpart (15). Though the results obtained in Theorems 2.6 and 2.7 corresponding to (29) are less general than (6), they never the less cover many interesting applications. In Section 4, we will present one financial example that satisfy the conditions (19), (20) for its dynamics of the state being the form of (29).…”

Section: Jingtao Shi and Huanshui Zhangmentioning

confidence: 99%

Stochastic recursive optimal control problem with time delay and applications

Shi¹,

Jin²,

Zhang³

2015

Mathematical Control &Amp; Related Fields

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This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution to a backward SDDE (BSDDE). When there are only the pointwise and distributed time delays in the state variable, a generalized Hamilton-Jacobi-Bellman (HJB) equation for the value function in finite dimensional space is obtained, applying dynamic programming principle. This generalized HJB equation admits a smooth solution when the coefficients satisfy a particular system of first order partial differential equations (PDEs). A sufficient maximum principle is derived, where the adjoint equation is a forward-backward SDDE (FBSDDE). Under some differentiability assumptions, the relationship between the value function, the adjoint processes and the generalized Hamiltonian function is obtained. A consumption and portfolio optimization problem with recursive utility in the financial market, is discussed to show the applications of our result. Explicit solutions in a finite dimensional space derived by the two different approaches, coincide.

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Section: Jingtao Shi and Huanshui Zhangmentioning

confidence: 99%

Stochastic recursive optimal control problem with time delay and applications

Shi¹,

Jin²,

Zhang³

2015

Mathematical Control &Amp; Related Fields

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“…Extension of the present work to the delayed case could be of interest. Such results were derived in [15], in the case of no regime-switching.…”

Section: Resultsmentioning

confidence: 83%

“…, D, ∇ θ 2 H = 0 i.e., − ln(1 + θ * 2 )(t, ζ) = −K(·, ζ), ν α -a.e. On the hand, one can show using product rule (see e.g., [15]) that Y given by (??) is solution to the following linear BSDE for each t and ω, with g(θ) := h(θ)…”

Section: )mentioning

confidence: 99%

“…Our paper is also motivated by the idea developed in [15,14,16], where the authors derive a general maximum principle for forward-backward stochastic differential games, stochastic differential games with delay and Markov regime-switching stochastic control with partial information, respectively. One important advantage of our approach is that we may relax the assumption of concavity on our Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

Pamen

Momeya

2017

Math Meth Oper Res

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In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for nonzerosum stochastic differential games problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for nonzero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty and to find optimal investment of an insurance firm under model uncertainty.Keywords Forward-backward stochastic differential equations · Markov regimeswitching · Stochastic differential games · Optimal investment · Stochastic maximum principleThe project on which this publication is based has been carried out with funding

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“…We can solve the anticipated BSDE in (5.4) recursively. This method can also be found in Menoukeu-Pamen (2013). Then, the unique solution (u(·), v(·)) defined by (5.3) is reduced to…”

Section: An Examplementioning

confidence: 99%

H₂/H_∞control for stochastic systems with delay

Qixia

2015

International Journal of Control

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This paper is concerned with the H 2 /H ∞ control problem for stochastic linear systems with delay in state, control and external disturbance-dependent noise. A necessary and sufficient condition for the existence of a unique solution to the control problem is derived. The resulting solution is characterised by a kind of complex generalised forward-backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the equivalent feedback solution via a new type of Riccati equations. To explain the theoretical results, we apply them to a population control problem.

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Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach

Cited by 33 publications

References 35 publications

Stochastic recursive optimal control problem with time delay and applications

Stochastic recursive optimal control problem with time delay and applications

A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

H₂/H_∞control for stochastic systems with delay

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Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach

Cited by 33 publications

References 35 publications

Stochastic recursive optimal control problem with time delay and applications

Stochastic recursive optimal control problem with time delay and applications

A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

H2/H∞control for stochastic systems with delay

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Product

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H₂/H_∞control for stochastic systems with delay