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We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…

Machine Learning · Computer Science 2025-12-18 Hanqing Jin , Renyuan Xu , Yanzhao Yang

We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…

Probability · Mathematics 2022-11-04 Erhan Bayraktar , Zhenhua Wang , Zhou Zhou

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

Probability · Mathematics 2008-12-20 Seid Bahlali

We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…

Optimization and Control · Mathematics 2024-10-03 Nicole El Karoui , Xiaolu Tan

Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…

Machine Learning · Computer Science 2021-03-02 Christian Wildner , Heinz Koeppl

This paper studies a {\it reversible} investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as…

Probability · Mathematics 2013-07-08 Salvatore Federico , Huyen Pham

We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…

Optimization and Control · Mathematics 2017-07-07 Erhan Bayraktar , Christopher W. Miller

In this article, we study optimal investment and consumption in an incomplete stochastic factor model for a power utility investor on the infinite horizon. When the state space of the stochastic factor is finite, we give a complete…

Mathematical Finance · Quantitative Finance 2025-09-12 Florian Gutekunst , Martin Herdegen , David Hobson

In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…

Numerical Analysis · Mathematics 2024-09-04 Josef Dick , Hecong Gao , William McLean , Kassem Mustapha

In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…

Optimization and Control · Mathematics 2023-09-19 Somnath Pradhan , Serdar Yuksel

We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…

Optimization and Control · Mathematics 2023-05-22 Jodi Dianetti , Giorgio Ferrari

We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…

Optimization and Control · Mathematics 2007-05-23 Erhan Bayraktar , Masahiko Egami

For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…

Numerical Analysis · Mathematics 2026-01-15 Constantin Bacuta

We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…

Statistics Theory · Mathematics 2011-12-30 Marc Hoffmann , Axel Munk , Johannes Schmidt-Hieber

We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…

Probability · Mathematics 2020-12-07 Hugh Entwistle , Christopher Lustri , Georgy Sofronov

This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the…

Optimization and Control · Mathematics 2016-08-02 Qingshuo Song , Chao Zhu

Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…

Numerical Analysis · Mathematics 2024-11-22 Faezeh Nassajian Mojarrad

We study an infinite horizon optimal stopping problem which arises naturally in the optimal timing of a firm/project sale or in the valuation of natural resources: the functional to be maximised is a sum of a discounted running reward and a…

Optimization and Control · Mathematics 2016-12-08 Jan Palczewski , Lukasz Stettner

In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…

Computational Finance · Quantitative Finance 2015-03-19 Sören Christensen

In this paper, we study the existence of an optimal strategy for the stochastic control of diffusion in general case and a saddle-point for zero-sum stochastic differential games. The problem is formulated as an extended BSDE with…

Probability · Mathematics 2011-11-09 Khaled Bahlali , Brahim El Asri