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Lithuanian Mathematical Journal

, Volume 49, Issue 1, pp 55–61 | Cite as

A property of the renewal counting process with application to the finite-time ruin probability

  • J. Kočetova
  • R. Leipus
  • J. Šiaulys
Article

Abstract

We consider the renewal counting process \( \mathit{\Theta} \left( t \right) = \sup \left\{ {n \geqslant 1:\theta_1 + \cdots + \theta_n \leqslant t} \right\} \), where θ 1 , θ 2 ,… are nonnegative independent identically distributed nondegenerate random variables with finite mean. The asymptotics for the tail of the exponential moment are derived. The obtained results are applied to the finite-time ruin probability in a renewal risk model.

Keywords

counting process renewal counting process large deviations finite-time ruin probability 

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Institute of Mathematics and InformaticsVilniusLithuania

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