Precise large deviations of aggregate claims with arbitrary dependence between claim sizes and waiting times

Yiqing Chen, Toby White and Kam Chuen Yuen

Insurance: Mathematics and Economics, 2021, vol. 97, issue C, 1-6

Abstract: Consider a renewal risk model in which claim sizes and interarrival times correspondingly form a sequence of independent, identically distributed, and nonnegative random pairs with a generic pair (X,θ). Chen and Yuen (2012) studied precise large deviations of aggregate claims in this model under the assumption that (X,θ) obeys a dependence structure described via a stochastic boundedness condition on the waiting time θ for a large claim X. That assumption unfortunately leads to asymptotic independence between X and θ and hence considerably limits the usefulness of the result obtained there. In this short paper, we make an effort to avoid that assumption by allowing X and θ to be arbitrarily dependent. As by-products, we propose two novel applications of the main result, one to pricing insurance futures and the other to approximating both the value at risk and expected shortfall of aggregate claims.

Keywords: Asymptotics; Consistent variation; Dependence; Renewal counting process; Uniformity (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:97:y:2021:i:c:p:1-6

DOI: 10.1016/j.insmatheco.2020.12.003

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