Related papers: Optimal stopping of strong Markov processes
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy…
Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…
Lewis and Mordecki have computed the Wiener-Hopf factorization of a L\'evy process whose restriction on $]0,+\infty[$ of their L\'evy measure has a rational Laplace transform. That allows to compute the distribution of $(X_t,\inf_{0\leq…
In the spirit of [Surya07'], we develop an average problem approach to prove the optimality of threshold type strategies for optimal stopping of L\'evy models with a continuous additive functional (CAF) discounting. Under spectrally…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
Under the hypothesis of convergence in probability of a sequence of c\`{a}dl\`{a}g processes $(X^n)\_n$ to a c\`{a}dl\`{a}g process $X$, we are interested in the convergence of corresponding values in optimal stopping and also in the…
The objective in this paper is to obtain fast converging reinforcement learning algorithms to approximate solutions to the problem of discounted cost optimal stopping in an irreducible, uniformly ergodic Markov chain, evolving on a compact…
The optimal zero delay coding of a finite state Markov source is considered. The existence and structure of optimal codes are studied using a stochastic control formulation. Prior results in the literature established the optimality of…
We consider optimal stopping problems with finite-time horizon and state-dependent discounting. The underlying process is a one-dimensional linear diffusion and the gain function is time-homogeneous and difference of two convex functions.…
In the paper we study continuous time controlled Markov processes using discrete time controlled Markov processes. We consider long run functionals: average reward per unit time or long run risk sensitive functional. We also investigate…
This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine…
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…
We extend the classical setting of an optimal stopping problem under full information to include for problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the…
In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman…
We prove the Wiener-Hopf factorization for Markov Additive processes. We derive also Spitzer-Rogozin theorem for this class of processes which serves for obtaining Kendall's formula and Fristedt representation of the cumulant matrix of the…
Let X_t, 0<=t<=T be a one-dimensional stochastic process with independent and stationary increments. This paper considers the problem of stopping the process X_t "as close as possible" to its eventual supremum M_T:=sup{X_t: 0<=t<=T}, when…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
We combine the fields of heuristic optimization and optimal stopping. We propose a strategy for benchmarking randomized optimization algorithms that minimizes the expected total cost for obtaining a good solution with an optimal number of…
We propose the entropy of random Markov trajectories originating and terminating at a state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary…