Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations

Øksendal, Bernt; Sulem, Agnès; Zhang, Tusheng

doi:10.1017/s0001867800004997

Cited by 49 publications

(75 citation statements)

References 11 publications

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“…And another direction, the adjoint equation is given by a time‐advanced backward stochastic differential equation. Some representative works in this direction, to name a few, include . In particular, Zhu and Zhang used a clever construction of the Hamiltonian function to obtain a system of three‐coupled BSDEs as the adjoint equation and cleared away the constrained condition in that one of the adjoint processes is equal to zero.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Problem for Risk‐Sensitive Mean‐Field Stochastic Delay Differential Equation with Partial Information

Liu

2017

Asian Journal of Control

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This paper deals with the risk-sensitive control problem for mean-field stochastic delay differential equations (MF-SDDEs) with partial information. Firstly, under the assumptions that the control domain is not convex and the value function is non-smooth, we establish a stochastic maximum principle (SMP). Then, by means of Itô's formula and some continuous dependence, we prove the existence and uniqueness results for another type of MF-SDDEs. Meanwhile, the verification theorem for the MF-SDDEs is obtained by using a clever construction of the Hamiltonian function. Finally, based on our verification theorem, a linear-quadratic system is investigated and the optimal control is also derived by the stochastic filtering technique.Key Words: Stochastic maximum principle, risk-sensitive control, mean-field type, stochastic delay differential equations, continuous dependence theorem.)However, in the macroscopic level, by considering the mass effect of such delayed particle systems, we can obtain the following MF-SDDEs Heping Ma received the Bachelor degree in applied mathematics from Anyang

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Section: Introductionmentioning

confidence: 99%

Optimal Control Problem for Risk‐Sensitive Mean‐Field Stochastic Delay Differential Equation with Partial Information

Liu

2017

Asian Journal of Control

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“…The problem, we are aiming at solving is the following: Remark 4.6. Let us mention that the time-advance BSDE (4.39) is linear and p and then has a solution; See for e.g., [10,15]. Let us also mention that for particular choices of the coefficient, we get the results of [8, Theorem 2.1] and obtain also the generalization to the stochastic interest rate.…”

Section: Optimal Premium Policy Of An Insurance Firm Under Stochasticmentioning

confidence: 87%

“…Such models may be identified as stochastic delay differential equations (SDDEs for short). For more information on delayed systems, the reader may consult for e.g., [11] and for optimal control for stochastic delay differential equations see for e.g., [15] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Optimal premium policy of an insurance firm with delay and stochastic interest rate

Mahera¹,

Pamen²,

Mwale³

2014

COSA

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In this paper, we study the optimization problem confronted by an insurance firm whose management can control its cash-balance dynamics by adjusting the underlying premium rate. The firm's objective is to minimize the total deviation of its cash-balance process to some pre-set target levels by selecting an appropriate premium policy. We study the problem in a general framework assuming the state process is governed by a stochastic delay differential equation and the classical utility function being replaced by a recursive utility or stochastic differential utility (SDU). We derive a sufficient maximum principle for an optimal control of such a system and apply the result to discuss some optimal premium rate control problems.

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“…These optimal control problems for stochastic systems with delays have been thoroughly investigated in recent years (see [1,7,13,25,26,34,35]). However, to the best of our knowledge, none of these results include our case.…”

Section: Introductionmentioning

confidence: 99%

“…However, to the best of our knowledge, none of these results include our case. References [1,7,25,26] established the stochastic maximum principles. Reference [1] showed a maximum principle of infinite horizon optimal control for stochastic delay equations.…”

Section: Introductionmentioning

confidence: 99%

A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation

Zhou

2018

ESAIM: COCV

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In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton−Jacobi−Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including time t and identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.

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Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations

Cited by 49 publications

References 11 publications

Optimal Control Problem for Risk‐Sensitive Mean‐Field Stochastic Delay Differential Equation with Partial Information

Optimal Control Problem for Risk‐Sensitive Mean‐Field Stochastic Delay Differential Equation with Partial Information

Optimal premium policy of an insurance firm with delay and stochastic interest rate

A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation

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