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Rough descriptions of ruin for a general class of surplus processes

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Harri Nyrhinen
Harri Nyrhinen*
Affiliation:
University of Helsinki
*
∗ Postal address: Rolf Nevanlinna Institute, P.O. Box 4, FIN-00014 University of Helsinki, Finland. Email address: [email protected]
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Abstract

Let {Yn | n = 1, 2,…} be a stochastic process and M a positive real number. Define the time of ruin by T = inf{n | Yn > M} (T = +∞ if Yn ≤ M for n = 1, 2,…). Using the techniques of large deviations theory we obtain rough exponential estimates for ruin probabilities for a general class of processes. Special attention is given to the probability that ruin occurs up to a certain time point. We also generalize the concept of the safety loading and consider its importance to ruin probabilities.

Keywords

Ruin problemlarge deviations theory

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60F10: Large deviations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998 , pp. 1008 - 1026
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Partially supported by the Research Grants Committee of the University of Helsinki.

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