Finding solutions to the Bellman equation often relies on restrictive boundedness assumptions. In this paper we develop a method of proof that allows to dispense with the assumption that returns are bounded from above. In applications our assumptions only imply that long run average (expected)...

Finding solutions to the Bellman equation relies on restrictive boundedness assumptions. The literature on endogenous growth or business cycle models with unbounded random shocks provide with numerous examples of recursive programs in which returns are not bounded along feasible paths. In this...

Finding solutions to the Bellman equation often relies on restrictive boundedness assumptions. In this paper we develop a method of proof that allows to dispense with the assumption that returns are bounded from above. In applications our assumptions only imply that long run average (expected)...

Background: The renewal function is widely useful in the areas of reliability, maintenance and spare components inventory planning. Its calculation relies on the type of the probability density function of component failure times which can be, regarding the region of the component lifetime,...

In this paper, we survey a portion of the literature in the analysis of warranty costs. In order to compare the price of different warranty policies, we review a framework which leads to expressing the expected costs in terms of complex functions arising in renewal theory. These functions and...

The paper considers a renewal risk process in which a given inter-arrival time possibly has an impact on the size of the resulting claim. Under a fairly general dependency structure which contains various well-known examples in the literature as special cases, recursive formulas for the moments...

A simple but effective approximation is proposed to compute the renewal function, M(t), and its integral. The asymptotic approximation of the renewal function and its integral, which are widely used in decision makings involving a renewal process, may not perform well when t is not large enough....

It is hard to find explicit expressions for the renewal function U(x)=∑n=0∞F∗n(x). Many researchers have made attempts to find suitable approximations for U(x). In this paper we present simple approximations and show that they cover many of the known results.

We consider a positive recurrent Markov chain on R+ with asymptotically zero drift which behaves like −c1/x at infinity; this model was first considered by Lamperti. We are interested in tail asymptotics for the stationary measure. Our analysis is based on construction of a harmonic function...