Related papers: General Optimal Stopping with Linear Costs
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.
The paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in…
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 article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using…
This paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics…
Given a spectrally negative L\'evy process $X$ drifting to infinity, (inspired on the early ideas of Shiryaev (2002)) we are interested in finding a stopping time that minimises the $L^p$ distance ($p>1$) with $g$, the last time $X$ is…
In this paper, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and M supplies in R in the case where the cost function is concave. The…
This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…
This paper studies function approximation for finite horizon discrete time Markov decision processes under certain convexity assumptions. Uniform convergence of these approximations on compact sets is proved under several sampling schemes…
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…
Explicit solution of an infinite horizon optimal stopping problem for a Levy processes with a polynomial reward function is given, in terms of the overall supremum of the process, when the solution of the problem is one-sided. The results…
We propose a method based on continuous time Markov chain approximation to compute the distribution of Parisian stopping times and price Parisian options under general one-dimensional Markov processes. We prove the convergence of the method…
We present an elementary state augmentation method for a class of static risk measure applied to the total cost for both Markov decision processes and stochastic optimal control, such that dynamic programming equations can be derived on the…
This paper presents a new condition for the existence of optimal stationary policies in average-cost continuous-time Markov decision processes with unbounded cost and transition rates, arising from controlled queueing systems. This…
The convex analytic method has proved to be a very versatile method for the study of infinite horizon average cost optimal stochastic control problems. In this paper, we revisit the convex analytic method and make three primary…
We study a discounted singular stochastic control problem driven by a general L\'evy process, where the objective is to minimize a cost functional composed of a running cost and a control cost that depends on the current state of the…
This paper concerns optimal stopping problems driven by the running maximum of a spectrally negative L\'{e}vy process $X$. More precisely, we are interested in modifications of the Shepp-Shiryaev optimal stopping problem [Avram, Kyprianou…
In this paper, we consider risk-sensitive discounted control problem for continuous-time jump Markov processes taking values in general state space. The transition rates of underlying continuous-time jump Markov processes and the cost rates…
We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience…
In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal…