Related papers: A probabilistic approach to continuous differentia…
We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear…
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…
We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients,…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
A moment constraint that limits the number of dividends in the optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense…
We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the…
The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…
In this article, the sufficient Pontryagin's maximum principle for infinite horizon discounted stochastic control problem is established. The sufficiency is ensured by an additional assumption of concavity of the Hamiltonian function.…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…
Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on…
We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…