Related papers: Dynamic Programming Principles for Optimal Stoppin…
We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is…
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
We consider a dynamic programming (DP) approach to approximately solving an infinite-horizon constrained Markov decision process (CMDP) problem with a fixed initial-state for the expected total discounted-reward criterion with a…
We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…
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…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
The combinatorial pricing problem (CPP) is a bilevel problem in which the leader maximizes their revenue by imposing tolls on certain items that they can control. Based on the tolls set by the leader, the follower selects a subset of items…
This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…
The optimal stopping problem is a category of decision problems with a specific constrained configuration. It is relevant to various real-world applications such as finance and management. To solve the optimal stopping problem,…
We address the crucial yet underexplored stability properties of the Hamilton--Jacobi--Bellman (HJB) equation in model-free reinforcement learning contexts, specifically for Lipschitz continuous optimal control problems. We bridge the gap…
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…
We use the geometry of suitably generalised potentials to solve risk-sensitive Markovian optimal stopping problems. As in the linear case due to Dynkin and Yushkievich (1967), the value function is the pointwise infimum of those functions…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
In this paper we study stochastic optimal control problems of fully coupled forward-backward stochastic differential equations (FBSDEs). The recursive cost functionals are defined by controlled fully coupled FBSDEs. We study two cases of…
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 a classical optimal stopping problem in continuous time, the agent can choose any stopping time without constraint. Dupuis and Wang (Optimal stopping with random intervention times, Advances in Applied Probability, 34, 141--157, 2002)…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
In this paper we focus on regional deterministic optimal control problems, i.e., problems where the dynamics and the cost functional may be different in several regions of the state space and present discontinuities at their interface.…
A new approach to feedback control design based on optimal control is proposed. Instead of expensive computations of the value function for different penalties on the states and inputs, we use a control Lyapunov function that amounts to be…