On a class of renewal risk processes. With discussion and a reply by the author. (English) Zbl 1081.60549

Dickson, David C. M.

N. Am. Actuar. J. 2, No. 3, 60-73 (1998).

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

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