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Pricing of Catastrophe Insurance Options Under Immediate Loss Reestimation

Part of: Mathematical economics Stochastic processes Miscellaneous applications of functional analysis

Published online by Cambridge University Press:  14 July 2016

Francesca Biagini ,
Yuliya Bregman  and
Thilo Meyer-Brandis
Francesca Biagini*
Affiliation:
Ludwig-Maximilians Universität München
Yuliya Bregman*
Affiliation:
Ludwig-Maximilians Universität München
Thilo Meyer-Brandis*
Affiliation:
University of Oslo
*
∗Postal address: Department of Mathematics, Ludwig-Maximilians Universität München, Theresienstrasse 39, D-80333 Munich, Germany.
∗Postal address: Department of Mathematics, Ludwig-Maximilians Universität München, Theresienstrasse 39, D-80333 Munich, Germany.
∗∗∗∗Postal address: CMA, University of Oslo, Postbox 1035, Blindern, Norway. Email address: meyerbr@math.uio.no
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Abstract

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We specify a model for a catastrophe loss index, where the initial estimate of each catastrophe loss is reestimated immediately by a positive martingale starting from the random time of loss occurrence. We consider the pricing of catastrophe insurance options written on the loss index and obtain option pricing formulae by applying Fourier transform techniques. An important advantage is that our methodology works for loss distributions with heavy tails, which is the appropriate tail behavior for catastrophe modeling. We also discuss the case when the reestimation factors are given by positive affine martingales and provide a characterization of positive affine local martingales.

Keywords

Catastrophe insurance optionloss indexFourier transformoption pricing formulaheavy tailpositive affine martingale

MSC classification

Secondary: 46N30: Applications in probability theory and statistics 60G07: General theory of processes 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 831 - 845
Copyright
Copyright © Applied Probability Trust 2008 

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