Related papers: A Time Consistent Formulation of Risk Constrained …
In this paper, we propose a unified stochastic optimal control framework that integrates time-optimal control problems with classical stochastic optimal control formulations. Unlike conventional deterministic time-optimal control models,…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
We consider sequences-indexed by time (discrete stages)-of families of multistage stochastic optimization problems. At each time, the optimization problems in a family are parameterized by some quantities (initial states, constraint…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
To investigate a time-consistent optimal strategy for the continuous time mean-variance model, we develop a new method to establish the Bellman principle. Based on this new method, we obtain a time-consistent dynamic optimal strategy that…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
We investigate discrete-time mean-variance portfolio selection problems viewed as a Markov decision process. We transform the problems into a new model with deterministic transition function for which the Bellman optimality equation holds.…
This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium,…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
We study the temporal robustness of stochastic signals. This topic is of particular interest in interleaving processes such as multi-agent systems where communication and individual agents induce timing uncertainty. For a deterministic…
This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time.…
We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite…
In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set…
In this paper we consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
This paper is concerned with the open-loop time-consistent solution of time-inconsistent mean-field stochastic linear-quadratic optimal control. Different from standard stochastic linear-quadratic problems, both the system matrices and the…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk…