×

zbMATH — the first resource for mathematics

On a class of renewal risk processes. With discussion and a reply by the author. (English) Zbl 1081.60549
Summary: I show how methods that have been applied to derive results for the classical risk process can be adapted to derive results for a class of risk processes in which claims occur as a renewal process. In particular, claims occur as an Erlang process. I consider the problem of finding the survival probability for such risk processes and then derive expressions for the probability and severity of ruin and for the probability of absorption by an upper barrier. Finally, I apply these results to consider the problem of finding the distribution of the maximum deficit during the period from ruin to recovery to surplus level 0.

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K05 Renewal theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Asmussen S., Insurance: Mathematics and Economics 10 pp 259– (1991)
[2] Cox D.R., Renewal Theory (1962)
[3] DOI: 10.1080/03461238.1984.10413758 · Zbl 0584.62174 · doi:10.1080/03461238.1984.10413758
[4] Dickson D.C.M., Working Paper No. 147 (1997)
[5] Gerber H.U., An Introduction to Mathematical Risk Theory (1979) · Zbl 0431.62066
[6] Gerber H.U., ASTIN Bulletin 17 pp 151– (1987) · doi:10.2143/AST.17.2.2014970
[7] Panjer H.H., Transactions of the XXIII International Congress of Actuaries pp 257– (1988)
[8] Picard P., Insurance: Mathematics and Economics 14 pp 107– (1994)
[9] Sparre Andersen E., Transactions of the XV International Congress of Actuaries 2 pp 219– (1957)
[10] Taka’cs L., Introduction to the Theory of Queues (1962)
[11] Thorin O., Scandinavian Actuarial Journal pp 65– (1982) · Zbl 0518.62084 · doi:10.1080/03461238.1982.10405105
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.