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Ruin estimation for a general insurance risk model

Part of: Applications Special processes

Published online by Cambridge University Press:  01 July 2016

Paul Embrechts  and
Hanspeter Schmidli
Paul Embrechts
Affiliation:
ETH Zurich
Hanspeter Schmidli*
Affiliation:
ETH Zurich
*
* Postal address: Department of Mathematics, ETH-Zentrum, CH-8092 Zürich, Switzerland.
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Abstract

The theory of piecewise-deterministic Markov processes is used in order to investigate insurance risk models where borrowing, investment and inflation are present.

Keywords

RISK THEORYRUINMARTINGALESPIECEWISE-DETERMINISTIC MARKOV PROCESSES

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 404 - 422
Copyright
Copyright © Applied Probability Trust 1994 

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References

Asmussen, S. and Rolski, T. (1991) Computational methods in risk theory: a matrix-algorithmic approach. Insurance Math. Econom. 10, 259–274.Google Scholar
Beard, R. E., Pentikäinen, T. and Pesonen, E. (1984) Risk Theory. Chapman and Hall, New York.Google Scholar
Dassios, A. and Embrechts, P. (1989) Martingales and insurance risk. Commun. Statist. Stoch. Models 5, 181–217.Google Scholar
Davis, M. H. A. (1984) Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models. J. R. Statist. Soc. B 46, 353–388.Google Scholar
Delbaen, F. and Haezendonck, J. (1987) Classical risk theory in an economic environment. Insurance Math. Econom. 6, 85–116.Google Scholar
Dellacherie, C. and Meyer, P. A. (1980) Probabilités et potentiel, Chapitre VI. Hermann, Paris.Google Scholar
Embrechts, P. (1990) Martingales in non-life insurance. Vilnius Conference Proceedings Vol. 1, 314–322. VNU Press.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. 2. Wiley, New York.Google Scholar
Gerber, H. U. (1979) An Introduction to Mathematical Risk Theory. Huebner Foundation Monographs, Philadelphia.Google Scholar
Grandell, J. (1991) Aspects of Risk Theory. Springer-Verlag, New York.Google Scholar
Ramlau-Hansen, H. (1988) A solvency study in non-life insurance I and II. Scand. Actuar. J. 3–34 and 35-59.Google Scholar
Spivak, M. (1979) A Comprehensive Introduction to Differential Geometry, Vol. 1. Publish or Perish, Houston, Texas.Google Scholar