Ruin probabilities expressed in terms of storage processes

Author:

Asmussen Søren,Petersen Søren Schock

Abstract

It is shown by a simple sample path argument that the ruin probabilities for a risk reserve process with premium rate p(r) depending on the reserve r and finite or infinite horizon are related in a simple way to the state probabilities of a compound Poisson dam with the same release rate p(r) at content r. In the infinite horizon case, this result has been established by Harrison and Resnick (1978), and in the finite horizon case with constant p it extends well-known relations to the M/G/1 virtual waiting time.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Reference11 articles.

1. Risk theory and the single server queue;Seal;Mitt. Verein Schweiz. Versich. Math.,1972

2. Schock Petersen S. (1988) Calculation of ruin probabilities when the premium depends on the current reserve. Submitted.

3. On the Ruin Problem of Collective Risk Theory

4. The Recurrence Classification of Risk and Storage Processes

5. Storage processes with general release rule and additive inputs

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