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Uniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models

Part of: Special processes Mathematical economics Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Yang Yang ,
Kaiyong Wang  and
Dimitrios G. Konstantinides
Yang Yang*
Affiliation:
Nanjing Audit University and Southeast University
Kaiyong Wang*
Affiliation:
Southeast University
Dimitrios G. Konstantinides*
Affiliation:
University of the Aegean
*
∗ Postal address: School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, China. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, Southeast University, Nanjing, 210096, China.
∗∗∗ Postal address: Department of Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, Greece. Email address: [email protected]
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Abstract

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In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

Keywords

Discounted aggregate claimdependenceLévy processconsistently varying taildominatedly varying taillong tailuniformity

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60G51: Processes with independent increments; L'evy processes 60K05: Renewal theory
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 669 - 684
Copyright
© Applied Probability Trust 

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