A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk {𝑋𝑛,𝑛=0,1,…} in the continuation region 𝐶:={1,2,…}, and the second player seeks to maximize the survival time in C. The process...

Fluid models are used to study functionals of the underlying random processes. Instead of analysing the trajectories, we investigate algebraic equations of the dynamic programming type which turn out to be discrete analogs of the corresponding differential equations. This analysis makes it...

Fluid models are used to study functionals of the underlying random processes. Instead of analysing the trajectories, we investigate algebraic equations of the dynamic programming type which turn out to be discrete analogs of the corresponding differential equations. This analysis makes it...

We consider the problem of a firm (“the buyer”) that must acquire a fixed number (L) of items. The buyer can acquire these items either at a fixed buy-it-now price in the open market or by participating in a sequence of NL auctions. The objective of the buyer is to minimize his expected...

This paper proposes a mathematical model for an optimal hostages rescue problem. When more than one person is taken hostage at a given time, a decision as to whether or not to attempt a rescue has to be made. The objective is to minimize the probability of a given number or more hostages being...

In this paper we study the optimal excess-of-loss reinsurance and dividend strategy for maximizing the expected total discounted dividends received by shareholders until ruin time. Transaction costs and taxes are required when dividends occur. The problem is formulated as a stochastic impulse...

In this work the problem of obtaining an optimal maintenance policy for a single-machine, single-product workstation that deteriorates over time is addressed, using Markov Decision Process (MDP) models. Two models are proposed. The decision criteria for the first model is based on the cost of...