arXiv subjects

Samy Mekkaoui

Publications and source records attributed to Samy Mekkaoui.

8 recordsLinked to original sources

arXiv2026

Stochastic Maximum Principle for McKean-Vlasov Control with Discrete Path Dependence

We study a class of McKean-Vlasov control problems with discrete path dependence. The coefficients and cost functional may depend on finitely many past values of the controlled state, observed at fixed deterministic times, and on their joint law. We establish well-posedness of the controlled state equation and derive necessary and sufficient optimality conditions through a stochastic Pontryagin maximum principle. The adjoint process is characterized by a backward stochastic differential equation with jumps at fixed observation times. Each jump represents the conditional sensitivity of future costs with respect to the corresponding observed state and its distribution. In the linear-quadratic case, we prove global solvability of the resulting forward-backward system by combining a continuation argument with a mean-field Riccati reduction. We finally discuss an application to time-series generation, where the terminal cost is given by a kernel-based discrepancy between the law of the sampled path and a target path distribution.

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arXiv2026

Deep-MKV-TS: Path-Dependent McKean--Vlasov Control for Financial Time Series Generation

We introduce Deep-MKV-TS, a path-dependent McKean-Vlasov framework for financial scenario generation. The stochastic dynamics are chosen by matching selected path and volatility features of generated scenarios to those observed in the data. Starting from an interpretable reference model, Deep-MKV-TS preserves the reference drift and adjusts its volatility, while a regularization penalty limits unnecessary departures from the calibrated dynamics. We solve the resulting control problem using a neural, sample-based implementation of the stochastic maximum principle. We validate the method against an exactly computable oracle. On Heston and Heston-mixture models, Deep-MKV-TS substantially reduces path-dependent and volatility-related deficiencies of the reference model. In delayed-volatility experiments, the correction remains effective as the forecasting horizon increases, while direct training becomes less reliable. On held-out intraday equity-index futures, the corrected model improves conditional forecasts relative to the reference and reaches a level of performance comparable to flexible generative and historical baselines. The resulting scenarios also support greater exposure than the reference under a fixed drawdown-risk target. These results show that path-dependent McKean-Vlasov control can enrich an interpretable reference model without replacing it.

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arXiv2026

Policy Gradient Learning for Distributionally Robust Markov Decision Processes under Wasserstein Ambiguity

We study finite-horizon Markov decision processes under distributional uncertainty in the transition kernels and develop a policy-gradient framework for Wasserstein distributionally robust control. Ambiguity is modeled by Wasserstein balls of common radius centered at state--action-dependent nominal transition kernels, leading to a max--min problem over randomized policies and admissible transition laws. Because the worst-case transition law depends implicitly on the policy parameters, the standard policy-gradient argument does not apply directly. We address this difficulty by combining the dynamic programming recursion with Wasserstein duality and a primal envelope argument. In general, the right and left directional derivatives of the one-step worst-case value are obtained by taking the minimum or maximum expected downstream value derivative over the set of worst-case transition laws. In finite state--action spaces, this set is characterized through the optimal face of a transport linear program, yielding an exact directional-derivative recursion. Under the required stability conditions and uniqueness of the active dual and transport optimizers, the derivative becomes linear in the policy perturbation and admits an explicit vector valued policy-gradient recursion. Building on this representation, we propose a robust actor--critic implementation and evaluate it on benchmark examples.

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arXiv2026

Optimal Control of Heterogeneous Mean-Field Stochastic Differential Equations with Common Noise and Applications

We initiate the study of optimal control problems of heterogeneous mean-field stochastic differential equations with common noise. We formulate the problem within a linear-quadratic framework, a particularly important class in control theory, typically renowned for its analytical tractability and broad range of applications. We derive a novel system of backward stochastic Riccati equations on infinite-dimensional Hilbert spaces. As this system is not covered by standard theory, we establish existence and uniqueness of solutions. We explicitly characterize the optimal control in terms of the solution of this system. We apply these results to solve two problems arising in mathematical finance: optimal trading with heterogeneous market participants and systemic risk in networks of heterogeneous banks.

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arXiv2026

Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approach

We propose a generative framework for learning stochastic dynamics from endpoint and intermediate distributional observations. The method formulates generation as a McKean-Vlasov control problem in which terminal and time-marginal laws are enforced through soft energy constraints. The associated optimality system is a forward-backward stochastic differential equation (FBSDE) whose backward component receives a continuous drift induced by the marginal law penalties. This provides a principled alternative to hard interpolation or optimal transport maps between observed distributions: the model learns a stochastic path law whose dynamics remain globally coupled through the mean-field objective. We derive the reduced FBSDE system for quadratic control cost and constant diffusion, connecting terminal and marginal law flat derivatives to score-like training signals. The resulting neural solver is evaluated on low-dimensional distributional benchmarks, where it recovers smooth stochastic paths matching prescribed marginal laws. In a higher-dimensional ALAE latent space, endpoint supervision is used as a qualitative stress test for transporting non-smiling faces toward smiling ones in a pretrained representation. We then use articulated human motion as a structured high-dimensional case study on a curated AMASS low-to-high position dataset, using SMPL-H pose sequences and reduced pose representations. The experiments show that soft marginal law constraints can produce coherent stochastic trajectories whose intermediate distributions follow the observed evolution of human motion. The code is available at https://github.com/murex/deep-mkv-gen/tree/main.

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arXiv2026

Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systems

We study the approximation of operators acting on probability measures on a product space with prescribed marginal. Let $I$ be a label space endowed with a reference measure $λ$, and define $\cal M_λ$ as the set of probability measures on $I\times \mathbb{R}^d$ with first marginal $λ$. By disintegration, elements of $\cal M_λ$ correspond to families of labeled conditional distributions. Operators defined on this constrained measure space arise naturally in mean-field control problems with heterogeneous, non-exchangeable agents. Our main theoretical result establishes a universal approximation theorem for continuous operators on $\cal M_λ$. The proof combines cylindrical approximations of probability measures with DeepONet-type branch-trunk neural architecture, yielding finite-dimensional representations of such operators. We further introduce a sampling strategy for generating training measures in $\cal M_λ$, enabling practical learning of such conditional mean-field operators. We apply the method to the numerical resolution of mean-field control problems with heterogeneous interactions, thereby extending previous neural approaches developed for homogeneous (exchangeable) systems. Numerical experiments illustrate the accuracy and computational effectiveness of the proposed framework.

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arXiv2026

Non-Exchangeable Mean Field Markov Decision Processes with common noise : from Bellman equation to quantitative propagation of chaos

We study infinite-horizon Markov Decision Processes (MDPs) with a continuum of heterogeneous agents interacting through a common noise, without assuming exchangeability. We introduce the framework of Conditional Non-Exchangeable Mean Field MDPs (CNEMF-MDPs) in both a strong formulation and a label-state formulation. We establish the equivalence between these two formulations by showing that the control problem can be lifted to a standard MDP defined on the Wasserstein space of probability measures over the product of the label and state spaces. Here, the label space represents agent heterogeneity, the state space is the individual state space, and a fixed distribution specifies the population of agent labels. Within this framework, we characterize the value function as the unique fixed point of an appropriate Bellman operator acting on this Wasserstein space. Our second contribution is a quantitative analysis of the propagation of chaos for this non-exchangeable setting with common noise. We derive sharp finite-population bounds by comparing the Bellman operator of the finite N-agent MDP, defined on the the N-fold product of the state space, with its infinite-agent counterpart. This comparison yields explicit constructions of near-optimal policies for the N-agent system from epsilon-optimal policies of the limiting CNEMF-MDP.

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arXiv2025

Stochastic maximum principle for optimal control problem of non exchangeable mean field systems

We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-quadratic case, where the optimal control is characterized by an infinite dimensional system of Riccati equations.

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