Let (?1,?1), (?2,?2),… be independent identically distributed R2-valued random vectors. We prove a strong law of large numbers, functional central limit theorem and the iterated logarithm for convergent perpetuities ?k?0b?1+…+?k? k+1 as b?1?. Under standard actuarial interpretation, these results correspond to situation when market is close customer-friendly scenario no risk.

This is an updated and enlarged version of Chapter 4 of the author’s Dynamic Programming and Optimal Control, Vol. II, 4th Edition, Athena Scientific, 2012. It includes new material, and it is substantially revised and expanded (it has more than doubled in size). The new material aims to provide a unified treatment of several models, all of which lack the contractive structure that is character...

A resource investment problem is a project-scheduling problem in which the availability levels of the resources are considered as decision variables and the goal is to find a schedule, and resource requirement levels, such that some objective function optimizes. In this paper, we consider a resource investment problem in which the goal is to maximize the net present value of the project cash fl...

Shapley’s discounted stochastic games, Everett’s recursive games and Gillette’s undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games. When the number of positions of the game is constant, our algorithms run in polynomial time.

A resource investment problem is a project-scheduling problem in which the availability levels of the resources are considered decision variables and the goal is to find a schedule and resource requirement levels such that some objective function optimizes. In this paper, we consider a resource investment problem in which the goal is to maximize the net present value of the project cash flows. ...

This article describes the results on the existence of optimal and nearly optimal policies for Markov Decision Processes (MDPs) with total expected discounted rewards. The problem of optimization of total expected discounted rewards for MDPs is also known under the name of discounted dynamic programming.