Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity

Hu, Mingshang; Ji, Shaolin

doi:10.1137/15m1037639

Cited by 24 publications

(18 citation statements)

References 37 publications

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“…Remark 5.2 In [3], the authors used the similar idea to obtain the variation equation for the cost functional associated with the stochastic recursive optimal control problem.…”

Section: Thus Supmentioning

confidence: 99%

Stein type characterization for $G$-normal distributions

Hu¹,

Péng²,

Song³

2017

Electron. Commun. Probab.

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“…Remark 5.2 In [3], the authors used the similar idea to obtain the variation equation for the cost functional associated with the stochastic recursive optimal control problem.…”

Section: Thus Supmentioning

confidence: 99%

Stein type characterization for $G$-normal distributions

Hu¹,

Péng²,

Song³

2017

Electron. Commun. Probab.

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“…Recently, Hu et al [12,13] developed the SDE and BSDE theory in this G-expectation framework. And they also studied the SMP for stochastic optimal control problems under G-expectation or uncertainty (see [11,15]).…”

Section: Introductionmentioning

confidence: 99%

“…As concerns previous works related with the SMP under sublinear expectation, we have to mention mainly the recent works by Biagini, Meyer-Brandis and Øksendal [2], Sun [23] and Hu and Ji [11]. In [2] the authors study a stochastic control problem (without mean-field term), composed of a forward G-SDE and a cost functional under G-expectations (also without meanfield term).…”

Section: Introductionmentioning

confidence: 99%

“…In the deduction of the sufficient optimality condition for a control û he uses convexity assumptions. Also in a non mean-field context, Hu and Ji [11] study a system of forward and backward G-SDEs, they consider as cost functional J(u) = Y u 0 , and they investigate the SMP. For this they show namely that the cost functional for the perturbed optimal control λ → J(û + λ(u − û)) is right-differentiable at λ = 0, and they use the special form of this derivative and an application of Sion's minimax theorem to derive a necessary optimality condition of the optimal control û.…”

Section: Introductionmentioning

confidence: 99%

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Mean field stochastic control under sublinear expectation

Buckdahn¹,

He²,

Li³

2022

Preprint

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Our work is devoted to the study of Pontryagin's stochastic maximum principle for a mean-field optimal control problem under Peng's G-expectation. The dynamics of the controlled state process is given by a stochastic differential equation driven by a G-Brownian motion, whose coefficients depend not only on the control, the controlled state process but also on its law under the G-expectation. Also the associated cost functional is of mean-field type. Under the assumption of a convex control state space we study the stochastic maximum principle, which gives a necessary optimality condition for control processes. Under additional convexity assumptions on the Hamiltonian it is shown that this necessary condition is also a sufficient one. The main difficulty which we have to overcome in our work consists in the differentiation of the G-expectation of parameterized random variables. As particularly delicate it turns out to handle with the G-expectation of a function of the controlled state process inside the running cost of the cost function. For this we have to study a measurable selection theorem for set-valued functions whose values are subsets of the representing set of probability measures for the G-expectation.

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“…Since Peng [8,9,10] established the fundamental theory of G-Brownian motion and SDEs driven by it (G-SDEs, in short), the study of G-expectation has received much attention, see a summary paper [11] and references within for details. The G-expectation has applied in many areas, for instance, stochastic optimization [5,6], financial markets with volatility uncertainty [3] and the Feyman-Kac formula [7].…”

Section: Introductionmentioning

confidence: 99%

Harnack Inequality and Gradient Estimate for $G$-SDEs with Degenerate Noise

Huang

Yang

2018

Preprint

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In this paper, the Harnack and shift Harnack inequalities for SDEs driven by G-Brownian motion (G-SDEs, in short) with degenerate noise are derived by method of coupling by change of measure. Moreover, the gradient estimate for the associated nonlinear semigroup Ptis also obtained for bounded measurable function f . Finally, the assertions are also proved for the degenerate functional G-SDEs. All of the above results extends the existed results in the linear expectation setting.

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Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity

Cited by 24 publications

References 37 publications

Stein type characterization for $G$-normal distributions

Stein type characterization for $G$-normal distributions

Mean field stochastic control under sublinear expectation

Harnack Inequality and Gradient Estimate for $G$-SDEs with Degenerate Noise

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