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Renewal theory
About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.
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31 citations
TL;DR: In this paper, the authors show that the optimal policy for a general Levy process with a Poisson renewal process is a band-policy, and for Cramer-Lundberg risk processes with exponential claim sizes and its diffusion limit, the policy collapses to a barrier-policy.
Abstract: Assume that the surplus process of an insurance company is described by a general Levy process and that possible dividend pay-outs to shareholders are restricted to random discrete times which are determined by an independent renewal process. Under this setting we show that the optimal dividend pay-out policy is a band-policy. If the renewal process is a Poisson process, it is further shown that for Cramer–Lundberg risk processes with exponential claim sizes and its diffusion limit the optimal policy collapses to a barrier-policy. Finally, a numerical example is given for which the optimal bands can be calculated explicitly. The random observation procedure studied in this paper also allows for an interpretation in terms of a random walk model with a certain type of random discounting.
31 citations
TL;DR: In this paper, the stationary distribution of a one-dimensional circuit-switched network was studied and it was shown that translation invariant arrival rates lead to a stationary distribution which can be described in terms of an alternating renewal process.
Abstract: This paper is concerned with the stationary distribution of a one-dimensional circuit-switched network. We show that if arrival rates decay geometrically with distance, then under the stationary distribution the number of circuits busy on successive links of the network at a fixed point in time is a Markov chain. When each link of the network has unit capacity we show that translation invariant arrival rates lead to a stationary distribution which can be described in terms of an alternating renewal process.
31 citations
01 Jan 1988
31 citations
TL;DR: An uncertainty distribution of delayed renewal process and an elementary delayed renewal theorem are given, which shows that the first interarrival time is quite different from the others.
Abstract: Delayed renewal process is a special type of renewal process in which the first interarrival time is quite different from the others. This paper first proposes an uncertain delayed renewal process whose interarrival times are regarded as uncertain variables. Then it gives an uncertainty distribution of delayed renewal process and an elementary delayed renewal theorem.
30 citations