A Pseudo-Markov Property for Controlled Diffusion Processes

Claisse, Julien; Talay, Denis; Tan, Xiaolu

doi:10.1137/151004252

Cited by 28 publications

(18 citation statements)

References 12 publications

(17 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…H k s dB s is of full measure under Pω for P−almost everyω ∈ Ω, and hence by the tower property P(A k ) = 1 for all k = 0, · · · , n (we also refer to [12] for some some discussion on the measurability of A k under Pω). This yields that…”

Section: Proof Of Theorem 24 (Ii) Under Assumption 23 (Iii)mentioning

confidence: 99%

Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints

Guo¹,

Tan²,

Touzi³

2016

SIAM J. Control Optim.

Self Cite

View full text Add to dashboard Cite

The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the weak formulation of the optimal Skorokhod embedding problem in Beiglböck, Cox & Huesmann [1] to the case of finitely-many marginal constraints 1 . Using the classical convex duality approach together with the optimal stopping theory, we establish some duality results under more general conditions than [1]. We also relate these results to the problem of martingale optimal transport under multiple marginal constraints.

show abstract

Section: Proof Of Theorem 24 (Ii) Under Assumption 23 (Iii)mentioning

confidence: 99%

Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints

Guo¹,

Tan²,

Touzi³

2016

SIAM J. Control Optim.

Self Cite

View full text Add to dashboard Cite

show abstract

“…As a consequence of the flow property in Lemma 3.1, we obtain the following conditioning lemma, also called pseudo-Markov property in the terminology of [20], for the controlled conditional distribution F 0 -progressive process {ρ…”

mentioning

confidence: 94%

Dynamic Programming for Optimal Control of Stochastic McKean--Vlasov Dynamics

Pham¹,

Wei²

2017

SIAM J. Control Optim.

131

113

View full text Add to dashboard Cite

We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field interaction under common noise. Our first main result is to state a dynamic programming principle for the value function in the Wasserstein space of probability measures, which is proved from a flow property of the conditional law of the controlled state process. Next, by relying on the notion of differentiability with respect to probability measures due to P.L. Lions [35], and Itô's formula along a flow of conditional measures, we derive the dynamic programming Hamilton-Jacobi-Bellman equation, and prove the viscosity property together with a uniqueness result for the value function. Finally, we solve explicitly the linear-quadratic stochastic McKean-Vlasov control problem and give an application to an interbank systemic risk model with common noise.MSC Classification: 93E20, 60H30, 60K35.

show abstract

“…In case of (1.7), the driving state is a CNM-SDE-BM and the lack of Markov property is due to non-anticipative functionals α and σ which may depend on the whole path of X u . In this case, the controlled state X u satisfies a pseudo-Markov property in the sense of [10]. The theory developed in this article applies to case (1.7) without requiring ellipticity conditions on the diffusion component σ.…”

Section: Andmentioning

confidence: 99%

Solving non-Markovian Stochastic Control Problems driven by Wiener Functionals

Leão,

Ohashi,

de Souza

2020

Preprint

View full text Add to dashboard Cite

In this article, we present a general methodology for stochastic control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main result of this paper is the development of a concrete method for characterizing and computing near-optimal controls for controlled Wiener functionals via a finite-dimensional approximation procedure. The theory does not require a priori functional differentiability assumptions on the value process and ellipticity conditions on the diffusion components. Explicit rates of convergence are provided under rather weak conditions for distinct types of non-Markovian and non-semimartingale states. The analysis is carried out on suitable finite dimensional spaces and it is based on the weak differential structure introduced by [38,39] jointly with measurable selection arguments. The theory is applied to stochastic control problems based on path-dependent SDEs and rough stochastic volatility models, where both drift and possibly degenerated diffusion components are controlled. Optimal control of drifts for path-dependent SDEs driven by fractional Brownian motion with exponent H ∈ (0, 1) is also discussed.

show abstract

A Pseudo-Markov Property for Controlled Diffusion Processes

Cited by 28 publications

References 12 publications

Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints

Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints

Dynamic Programming for Optimal Control of Stochastic McKean--Vlasov Dynamics

Solving non-Markovian Stochastic Control Problems driven by Wiener Functionals

Contact Info

Product

Resources

About