A Note on Some New Perpetuities

Scandinavian Actuarial Journal, Vol. 4, p. 261-270, 2005

13 Pages Posted: 6 Jan 2005 Last revised: 7 Oct 2008

See all articles by Marc Decamps

Marc Decamps

Katholieke Universiteit Leuven (KUL)

Ann De Schepper

University of Antwerp - Faculty of Applied Economics

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Wim Schoutens

KU Leuven - Department of Mathematics

Abstract

In a recent paper, Salminen and Yor (2004b) relate the distribution of the Dufresne's reflected perpetuity to the hitting time of a reflected Bessel process. In this contribution, we adapt the results of Salminen and Yor (2004b) in several ways. First, we use spectral theory to obtain a series expansion for the distribution that renders this quantity applicable to actuarial purposes. We also investigate perpetuities when the rate of return is modelled by a more general skew Brownian motion with drift.

Keywords: Skew Brownian motion, Bessel processes, local time, spectral theory, perpetuities

Suggested Citation

Decamps, Marc and De Schepper, Ann and Goovaerts, Marc and Schoutens, Wim, A Note on Some New Perpetuities. Scandinavian Actuarial Journal, Vol. 4, p. 261-270, 2005, Available at SSRN: https://ssrn.com/abstract=642963

Marc Decamps (Contact Author)

Katholieke Universiteit Leuven (KUL) ( email )

Oude Markt 13
Leuven, Vlaams-Brabant
Belgium

Ann De Schepper

University of Antwerp - Faculty of Applied Economics ( email )

Prinsstraat 13
Antwerp, B-2000
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

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