Local limit theorems for collective risk models

Hattacha Kongjiw, Petcharat Rattanawong and Kritsana Neammanee

Statistics & Probability Letters, 2023, vol. 201, issue C

Abstract: A probability model known as the collective risk model is used to describe the total claim from a portfolio of insurance contracts. It is essential to non-life insurance. Let N represent the number of claims and X1,X2,… represent the amount of loss in each claim where Xj′s are independent and identically distributed. For the collective risk model, the total claim is given by SN=X1+X2+⋯+XN. Local limit theorems estimate the probability at a particular point P(SN=k). In this paper, we provide local limit theorems for SN, where N is a random variable with a binomial, Poisson and negative binomial distribution. Our results give a better rate of convergence than Berry–Esseen’s Theorem. Explicit constants of the error bounds are also given.

Keywords: Local limit theorem; Collective risk model; Individual risk model; Compound binomial distribution; Compound Poisson distribution; Compound negative binomial distribution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109867

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