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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of finding two optimal stopping times: the best moment of change the parameters and the moment of maximal value of the capital assets, and they used a dynamic programming method to calculate the expected capital at that times.
Abstract: The following problem in risk theory is considered. An insurance company, endowed with an initial capital a>0, receives insurance premiums and pays out successive claims. The losses occur according to renewal process. At any moment, the company may broaden or narrow down the offer, what entails the change of the parameters. This change concerns the rate of income, the intensity of renewal process and the distribution of claims. After the change, the management wants to know the moment of the maximal value of the capital assets. Therefore, our goal is finding two optimal stopping times: the best moment of change the parameters and the moment of maximal value of the capital assets. We will use a dynamic programming method to calculate the expected capital at that times.

26 citations

Reference EntryDOI
15 Feb 2011
TL;DR: Point process models are useful for describing phenomena occurring at random locations and/or times as discussed by the authors, and some important models include Poisson processes, renewal processes, Hawkes processes, and Markovian point processes.
Abstract: Point process models are useful for describing phenomena occurring at random locations and/or times. Following a review of basic concepts, some important models are surveyed including Poisson processes, renewal processes, Hawkes processes, and Markovian point processes. Techniques for estimation, simulation, and residual analysis for point processes are also briefly discussed. Keywords: Poisson process; marked point process; Hawkes process; renewal process; conditional intensity; clustering density; maximum likelihood; residual analysis

26 citations

Journal ArticleDOI
TL;DR: In this paper, the distribution of the first time a prespecified level is reached or exceeded, and of the position at this time is derived for a process that increases linearly, with unit slope, between jumps of i.i.d. positive sizes occurring at renewal times.
Abstract: For a process that increases linearly, with unit slope, between jumps of i.i.d. positive sizes occurring at renewal times, we present methods to compute the distribution of the first time a prespecified level is reached or exceeded, and of the position at this time. In the exponential case the Laplace transform of this first-exit time is derived in closed form. A general formula for the distribution of the stopping time is given, and shown to yield explicit results in certain cases. An effective method of successive approximation is also derived. The problem is equivalent to that of determining the distribution of the total ON time in [0, t] of a system changing between the states ON and OFF at the points of an alternating renewal process.

26 citations

Journal ArticleDOI
TL;DR: This paper studies the probability distributions and statistical moments for the number of handovers per call for a variety of combinations of the call holding time (CHT) and cell residence time (CRT) distributions.

25 citations

Journal ArticleDOI
TL;DR: In this article, the mixed δ-shock models for the multi-state systems are generalized to a model for which the system switches to a lower partially working state as soon as the occurrence of each inte...
Abstract: In this paper, the mixed δ-shock models for the multi-state systems is generalized to a model for which the system switches to a lower partially working state as soon as the occurrence of each inte...

25 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202327
202260
202173
202083
201973
201886