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Asymptotics for a multidimensional risk model with a random number of delayed claims and multivariate regularly varying distribution

Part of: Applications Distribution theory

Published online by Cambridge University Press:  10 December 2025

Meng Yuan Open the ORCID record for Meng Yuan [Opens in a new window] ,
Dawei Lu Open the ORCID record for Dawei Lu [Opens in a new window]  and
Yu Fu
Meng Yuan*
Affiliation:
Dongbei University of Finance and Economics
Dawei Lu*
Affiliation:
Dalian University of Technology
Yu Fu*
Affiliation:
Dongbei University of Finance and Economics
*
*Postal address: School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian, China.
**Postal address: School of Mathematical Sciences, Dalian University of Technology, Dalian, China.
*Postal address: School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian, China.
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Abstract

This paper investigates a continuous-time multidimensional risk model with stochastic returns driven by a geometric Lévy process, where each main claim is accompanied by a random number of delayed claims. By employing a framework of multivariate regular variation for claim sizes and allowing for arbitrarily dependent claim-number processes, we conduct asymptotic analyses for two types of ruin probabilities. Numerical examples are used to demonstrate the accuracy of our asymptotic estimates.

Keywords

Asymptoticsdelayed claimsmultivariate regular variationruin probabilitystochastic return

MSC classification

Primary: 62E20: Asymptotic distribution theory
Secondary: 62P05: Applications to actuarial sciences and financial mathematics

Information

Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 30
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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