Asymptotics for a bidimensional risk model with two geometric Lévy price processes

Yang Yang; Kaiyong Wang; Jiajun Liu; Zhimin Zhang

doi:10.3934/jimo.2018053

Asymptotics for a bidimensional risk model with two geometric Lévy price processes

Yang Yang
, Kaiyong Wang
, Jiajun Liu
, Zhimin Zhang^*

^*Corresponding author for this work

Department of Financial and Actuarial Mathematics

Nanjing Audit University
Suzhou University of Science and Technology
Chongqing University

Research output: Contribution to journal › Article › peer-review

47 Citations (Scopus)

Abstract

Consider a bidimensional risk model with two geometric Lévy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric Lévy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.

Original language	English
Pages (from-to)	481-505
Number of pages	25
Journal	Journal of Industrial and Management Optimization
Volume	15
Issue number	2
DOIs	https://doi.org/10.3934/jimo.2018053
Publication status	Published - 1 Apr 2019

Keywords

Asymptotics
Bidimensional risk model
Consistently varying tail
Dependence
Dominatedly varying tail
Geometric Lévy price process
Infinite-time and finitetime ruin probabilities
Long tail

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10.3934/jimo.2018053

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title = "Asymptotics for a bidimensional risk model with two geometric L{\'e}vy price processes",

abstract = "Consider a bidimensional risk model with two geometric L{\'e}vy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric L{\'e}vy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.",

keywords = "Asymptotics, Bidimensional risk model, Consistently varying tail, Dependence, Dominatedly varying tail, Geometric L{\'e}vy price process, Infinite-time and finitetime ruin probabilities, Long tail",

author = "Yang Yang and Kaiyong Wang and Jiajun Liu and Zhimin Zhang",

note = "Publisher Copyright: {\textcopyright} 2019 American Institute of Mathematical Sciences.",

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AU - Liu, Jiajun

AU - Zhang, Zhimin

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N2 - Consider a bidimensional risk model with two geometric Lévy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric Lévy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.

AB - Consider a bidimensional risk model with two geometric Lévy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric Lévy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.

KW - Asymptotics

KW - Bidimensional risk model

KW - Consistently varying tail

KW - Dependence

KW - Dominatedly varying tail

KW - Geometric Lévy price process

KW - Infinite-time and finitetime ruin probabilities

KW - Long tail

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DO - 10.3934/jimo.2018053

M3 - Article

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EP - 505

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

IS - 2

ER -

Asymptotics for a bidimensional risk model with two geometric Lévy price processes

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Keywords

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