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We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…
As is well known, average-cost optimality inequalities imply the existence of stationary optimal policies for Markov Decision Processes with average costs per unit time, and these inequalities hold under broad natural conditions. This paper…
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…
This paper thoroughly investigates stochastic linear-quadratic optimal control problems with the Markovian regime switching system, where the coefficients of the state equation and the weighting matrices of the cost functional are random.…
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…
We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model where the drift and volatility coefficients are general functions of the level of surplus and the external…
This paper studies an $\alpha$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market…
This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously…
We consider a discrete-time dividend payout problem with risk sensitive shareholders. It is assumed that they are equipped with a risk aversion coefficient and construct their discounted payoff with the help of the exponential premium…
In this paper, we study the $m$-states optimal switching problem in finite horizon, when the switching cost functions are arbitrary and can be positive or negative. This has an economic incentive in terms of central evaluation in cases…
Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems.…
Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here,…
This tutorial describes recently developed general optimality conditions for Markov Decision Processes that have significant applications to inventory control. In particular, these conditions imply the validity of optimality equations and…
Under mean-variance-utility framework, we propose a new portfolio selection model, which allows wealth and time both have influences on risk aversion in the process of investment. We solved the model under a game theoretic framework and…
We consider killed Markov decision processes for countable models on a finite time-interval. Existence of a uniform $\varepsilon$-optimal policy is proven. We show the correctness of the fundamental equation. The optimal control problem is…
We consider a control problem for a finite-state Markov system whose performance is evaluated by a coherent Markov risk measure. For each policy, the risk of a state is approximated by a function of its features, thus leading to a…
We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…
In this paper, we address an optimal management problem of community energy storage in the real-time electricity market under a stochastic renewable environment. In a real-time electricity market, complete market information may not be…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
We design a dynamic rate scheduling policy of Markov type via the solution (a social optimal Nash equilibrium point) to a utility-maximization problem over a randomly evolving capacity set for a class of generalized processor-sharing queues…