Work

Asymptotic analysis of tail moment in a dependent risk model

Year: 2026

Type: article

Abstract: In this paper, we discuss a risk model with multiple business lines, where the log-discount process is a combination of a general adapted process with continuous paths and a compound stochastic jump process. We propose a dependence structure under the framework of multivariate regular variation, which not only captures the dependence among the insurance losses but also the one between the insurance losses and the financial jump sizes. We study a novel tail moment risk measure defined as the conditional moment of the present value of an individual business line's aggregate losses, given that the present value of aggregate losses of all business lines exceeds its Value-at-Risk. With the help of Extreme Value Theory, we derive asymptotic expansion of the tail moment. We illustrate the main results with some numerical studies which reveal that while the tail moment is notably impacted by the dependence structure, the heavy-tailedness plays a comparatively more significant role.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2026.131135

Authors: Lei Zou, Jiangyan Peng, Lanpeng Ji, Chenghao Xu

Institutions: University of Electronic Science and Technology of China, University of Leeds

Language: English

Topic: Probability and Risk Models

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: National Natural Science Foundation of China