Taiwanese Journal of Mathematics

THE NON-RUIN PROBABILITY FOR THE RISK RESERVE PROCESS WITH EXPONENTIAL TYPE CLAIMS

Ayumi Kishikawa and Makoto Doi

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Abstract

In this paper, we consider the risk reserve process with claims. In order to have the non-ruin probability in finite time, we use the skeleton process studied by T.Mikosch. Furthermore, we find a general formula that derives the non-ruin probability for the model in which the claim inter-arrival time has an exponential distribution and the claim size has an exponential distribution with distinct rate.

Article information

Source
Taiwanese J. Math., Volume 13, Number 4 (2009), 1343-1352.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405512

Digital Object Identifier
doi:10.11650/twjm/1500405512

Mathematical Reviews number (MathSciNet)
MR2543747

Zentralblatt MATH identifier
1180.37011

Subjects
Primary: 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 46N30: Applications in probability theory and statistics

Keywords
non-ruin probability risk reserve process skeleton process exponential claim size

Citation

Kishikawa, Ayumi; Doi, Makoto. THE NON-RUIN PROBABILITY FOR THE RISK RESERVE PROCESS WITH EXPONENTIAL TYPE CLAIMS. Taiwanese J. Math. 13 (2009), no. 4, 1343--1352. doi:10.11650/twjm/1500405512. https://projecteuclid.org/euclid.twjm/1500405512


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References

  • M. Doi, The Expected Ruin Time for a Storage Process, Mathematica Japonica, 51-1 (2000), 67-74.
  • M. Doi, The ruin probability for the storage process with large scale demands, Scientiae Mathematicae Japonicae, Online, e-2006 (2006), 595-601.
  • T. Mikosch, Non-life insurance mathematics, Springer, Berlin, 2004.