On the Distribution of Cash-Flows Using Esscher Transforms

15 Pages Posted: 2 Mar 2006

See all articles by David Vyncke

David Vyncke

Ghent University - Department of Applied Mathematics and Computer Science

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Ann De Schepper

University of Antwerp - Faculty of Applied Economics

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

Jan Dhaene

Katholieke Universiteit Leuven

Abstract

In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process and a shifted inverse Gaussian process to describe the logarithm of the stock price.In the present paper it is shown how upper and lower bounds in convex order can be obtained when we use these types of models to describe the stochastic accumulation factors for a given cash-flow.

Suggested Citation

Vyncke, David and Goovaerts, Marc and De Schepper, Ann and Kaas, Rob and Dhaene, Jan, On the Distribution of Cash-Flows Using Esscher Transforms. Journal of Risk and Insurance, Vol. 70, No. 3, pp. 563-575, 2003, Available at SSRN: https://ssrn.com/abstract=887021

David Vyncke (Contact Author)

Ghent University - Department of Applied Mathematics and Computer Science ( email )

Gent, 9000
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)

Ann De Schepper

University of Antwerp - Faculty of Applied Economics ( email )

Prinsstraat 13
Antwerp, B-2000
Belgium

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Jan Dhaene

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

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