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Operations Stochastiques de Capitalisation

Published online by Cambridge University Press:  29 August 2014

Pierre Devolder
Pierre Devolder*
Affiliation:
Royale Beige, Bruxelles
*
43, Boulevard Théo Lambert, B-1070 Bruxelles, Belgium
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Abstract

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This paper presents a stochastic model of capitalization which takes into account the financial risk in the actuarial processes.

We first introduce a stochastic differential equation which allows us to define the capitalization and actualization processes.

We use these concepts to present a new principle of premium calculation for the capitalization operations, based on the equality between backward reserve and conditional expectation of the forward reserve.

A generalization of the classical Thiele equation in life insurance is also given.

Numerical examples illustrate the model.

Type
Astin Competition 1985: Prize-Winning Papers and Other Selected Papers
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue S1 , April 1986 , pp. S5 - S30
Copyright
Copyright © International Actuarial Association 1986

References

Bibliographie

De Vylder, F. et Jaumain, C. (1976) Exposé moderne de la théorie mathémalique des opérations viagères. Office des Assureurs de Belgique.Google Scholar
Ginman, I.I. et Skorohod, A. V. (1972) Stochastic differential equations. Springer Verlag.CrossRefGoogle Scholar
Malliaris, A. G. et Brock, W. A. (1981) Stochastic methods in economics and Finance. North-Holland.Google Scholar
Pollard, J. H. (1971) On Fluctuating Interest Rates. Bulletin de l'Association Royale des Actuaires Beiges, No. 66Google Scholar
Saada, M. (1979) Traité pratique de mathématiques financières. Vuibert: Paris.Google Scholar
Schnieper, R. (1983) Risk Processes with Stochastic Discounting. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker, 2.Google Scholar