This paper uses linear programming to numerically evaluate the Laplace transform of the exit time distribution and the resolvent of the moments of various Markov processes in bounded regions. The linear programming formulation is developed from a martingale characterization of the processes and...

Binomial models of n-period financial markets are of considerable practical and theoretical interest since they allow, due to their completeness, hedging strategies and pricing formulas. Here we derive several maximum properties of these models within the class of models with general exponential...

We consider discrete time Markov Decision Process (MDP) with finite state and action spaces under average reward optimality criterion. The decomposition theory, in Ross and Varadarajan [11], leads to a natural partition of the state space into strongly communicating classes and a set of states...

In this paper, we consider a multi-item continuous review inventory system with compound Poisson demands under a general cost structure. Excess demand is backlogged and a fixed delivery lag is assumed. A new algorithm for computing an exact optimal policy is derived based upon the policy...

Optimal switching we consider is the following generalization of optimal stopping: (i) there are a reward function and a cost function on the state space of a Markov chain; (ii) a controller selects stopping times sequentially; (iii) at those times the controller receives rewards and pays costs...

A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods and inexact-Newton methods for solving the system of nonsmooth equations and for solving the system of equations of smooth compositions of nonsmooth functions, are developed. The...

We consider the optimal stopping of a linear diffusion in a problem subject to both a cumulative term measuring the expected cumulative present value of a continuous and potentially state-dependent profit flow and an instantaneous payoff measuring the salvage or terminal value received at the...

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points...

We consider semi-Markov control models (SMCMs) with a Borel state space satisfying certain stochastic stability assumptions on the transition structure which imply the so-called V-uniform geometric ergodicity of the state process. We deal with a class of ε-perturbations of transition...

This paper concerns the general capacity (GC) problem on metric spaces. Conditions are given under which the strong duality condition holds, that is, GC and its dual GC<Superscript>*</Superscript> are both solvable and their optimal values coincide. Copyright Springer-Verlag Berlin Heidelberg 2001