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Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims

Part of: Stochastic processes Mathematical economics Applications

Published online by Cambridge University Press:  01 July 2016

C. C. Heyde  and
Dingcheng Wang
C. C. Heyde
Affiliation:
Australian National University and Columbia University
Dingcheng Wang*
Affiliation:
Australian National University and University of Electronic Science and Technology of China
*
∗∗ Postal address: Center of Financial Mathematics, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia. Email address: [email protected]
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Abstract

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By expressing the discounted net loss process as a randomly weighted sum, we investigate the finite-time ruin probabilities for the Poisson risk model with an exponential Lévy process investment return and heavy-tailed claims. It is found that in finite time, however, the extreme of insurance risk dominates the extreme of financial risk, but, for the case of dangerous investment (see Klüppelberg and Kostadinova (2008) for an accurate definition of dangerous investment), the extreme of financial risk has more and more of an effect on the total risk, and as time passes, the extreme of financial risk finally dominates the extreme of insurance risk.

Keywords

Finite-time ruin probabilityinvestment returnLévy processPoisson risk modelself-financing portfolioregularly varying tailclaim

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 91B30: Risk theory, insurance
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 1 , March 2009 , pp. 206 - 224
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

∗

C. C. Heyde died in March 2008.

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