Computing Compound Distributions Faster!

12 Pages Posted: 17 Sep 2007

See all articles by Peter den Iseger

Peter den Iseger

Cardano Risk Management

M.A.J. Smith

Erasmus University Rotterdam (EUR) - Department of Econometrics

Rommert Dekker

Erasmus University, Rotterdam (EUR) - Erasmus School of Economics ; Econometric Institute; Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM) ; Tinbergen Institute Rotterdam

Abstract

The use of Panjer's algorithm has meanwhile become a widespread standard technique for actuaries (Kuon et al., 1955). Panjer's recursion formula is used for the evaluation of compound distributions and can be applied to life and general insurance problems. The discrete version of Panjer's recursion formula is often applied to continuous distributions by discretizing the underlying distribution at n equidistant points, covering a large enough interval, say [0, n\Delta]. Panjer's recursion returns discrete function as an approximation of the compound distribution. It is claimed that this procedure is fast, (O(n^2)), accurate (O(\Delta^2)) and easy to understand, cf. Btthlmann (1984), Dickson (1995) and Xie (1989). In this article we propose a method based on cubic splines. The accuracy of the method is better, namely O(\Delta^5). The computation time is O(n^2) and hence for the same accuracy much faster and furthermore, the method returns a twice continuously differentiable function.

Keywords: Recursions, Compound distributions, Compound Poisson process, Insurance Mathematics

Suggested Citation

Iseger, Peter den and Smith, M.A.J. and Dekker, Rommert and Dekker, Rommert, Computing Compound Distributions Faster!. Insurance: Mathematics and Economics, Vol. 20, 1997, Available at SSRN: https://ssrn.com/abstract=1014801

Peter den Iseger (Contact Author)

Cardano Risk Management ( email )

Rotterdam 3011 AA
Netherlands
+31 10 2434747 (Phone)

HOME PAGE: http://www.cardano.com

M.A.J. Smith

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

Postbus 1738
P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 4081275 (Phone)
+31 10 4527347 (Fax)

Rommert Dekker

Erasmus University, Rotterdam (EUR) - Erasmus School of Economics ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands
+31 10 408 1274 (Phone)
+31 10 408 9162 (Fax)

HOME PAGE: http://www.few.eur.nl/few/people/rdekker/

Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

HOME PAGE: http://https://www.eur.nl/people/rommert-dekker

Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Tinbergen Institute Rotterdam ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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