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A Discrete Time Benchmark Approach for Insurance and Finance

Published online by Cambridge University Press:  17 April 2015

Hans Bühlmann  and
Eckhard Platen
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Abstract

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This paper proposes a consistent approach to discrete time valuation in insurance and finance. This approach uses the growth optimal portfolio as reference unit or benchmark. When used as benchmark, it is shown that all benchmarked price processes are supermartingales. Benchmarked fair price processes are characterized as martingales. No measure transformation is needed for the fair pricing of insurance policies and derivatives. The standard actuarial pricing rule is obtained as a particular case of fair pricing when the contingent claim is independent from the growth optimal portfolio.

1991 Mathematics Subject Classification: primary 90A12 secondary 60G30, 62P20

JEL Classification: G10, G13

Keywords

Financial and insurance market modelbenchmark approachgrowth optimal portfolionumeraire portfoliofair pricingactuarial pricingunit linked insurance

Information

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 153 - 172
Copyright
Copyright © ASTIN Bulletin 2003

Footnotes

1

Department of Mathematics, Eidgenössische Technische Hochschule, 8092 Zürich, Switzerland.

2

University of Technology Sydney, School of Finance & Economics and Department of Mathematical Sciences, PO Box 123, Broadway, NSW, 2007, Australia.

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