Journal of Applied Probability

Uniform asymptotics for discounted aggregate claims in dependent risk models

Yang Yang, Kaiyong Wang, and Dimitrios G. Konstantinides

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51, Number 3 (2014), 669-684.

Dates
First available in Project Euclid: 5 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1409932666

Digital Object Identifier
doi:10.1239/jap/1409932666

Mathematical Reviews number (MathSciNet)
MR3256219

Zentralblatt MATH identifier
1303.91097

Subjects
Primary: 91B30: Risk theory, insurance
Secondary: 60G51: Processes with independent increments; Lévy processes 60K05: Renewal theory

Keywords
Discounted aggregate claim dependence Lévy process consistently varying tail dominatedly varying tail long tail uniformity

Citation

Yang, Yang; Wang, Kaiyong; Konstantinides, Dimitrios G. Uniform asymptotics for discounted aggregate claims in dependent risk models. J. Appl. Probab. 51 (2014), no. 3, 669--684. doi:10.1239/jap/1409932666. https://projecteuclid.org/euclid.jap/1409932666


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