Related papers: Dynamic programming equation for the mean field op…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is…
This paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics…
The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). To this end, we first prove a stochastic…
The dynamic time warping (dtw) distance is an established tool for mining time series data. The DTW-Mean problem consists of computing a series which minimizes the so-called Fr\'echet function, that is, the sum of squared dtw-distances to a…
We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…
We consider a general class of mean field control problems described by stochastic delayed differential equations of McKean-Vlasov type. Two numerical algorithms are provided based on deep learning techniques, one is to directly…
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…
We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…
This paper deals with unconstrained discounted continuous-time Markov decision processes in Borel state and action spaces. Under some conditions imposed on the primitives, allowing unbounded transition rates and unbounded (from both above…
Dynamic time warping constitutes a major tool for analyzing time series. In particular, computing a mean series of a given sample of series in dynamic time warping spaces (by minimizing the Fr\'echet function) is a challenging computational…
This paper studies the problem of optimal switching for one-dimensional diffusion, which may be regarded as sequential optimal stopping problem with changes of regimes. The resulting dynamic programming principle leads to a system of…
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical…
We prove the dynamic programming principle for a class of diffusion processes controlled up to the time of exit from a cylindrical region $[0,T)\times G$. It is assumed that the functional to be maximized is in the Lagrange form with…
We study a fully-coupled system of conditional slow-fast McKean-Vlasov Stochastic Differential Equations that exhibit full dependence on both the slow and fast components, as well as on the conditional law of the slow component. Our aim is…
We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such…
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal…
This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in [30]. We extend the applicability of the theory by relaxing compactness and boundedness…
We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with…