Approximation of Ruin Probabilities via Erlangized Scale Mixtures

Peralta, O, Rojas-Nandayapa, L, Xie, W and Yao, H Approximation of Ruin Probabilities via Erlangized Scale Mixtures. Insurance: Mathematics and Economics. ISSN 0167-6687 (Submitted)

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Abstract

In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cram\'er--Lundberg reserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale mixtures (ESM) and correspond to nonnegative and absolutely continuous distributions which can be written as a Mellin--Stieltjes convolution $\Pi\star G$ of a nonnegative distribution $\Pi$ with an Erlang distribution $G$. A distinctive feature of such a class is that it contains heavy-tailed distributions. We suggest a simple methodology for constructing a sequence of distributions having the form $\Pi\star G$ to approximate the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size distribution is modelled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed.

Item Type:	Article
Uncontrolled Keywords:	math.PR, math.PR
Depositing User:	Symplectic Admin
Date Deposited:	31 May 2017 09:25
Last Modified:	19 Jan 2023 07:03
Related URLs:	http://arxiv.org/abs/1705.09405v1
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3007725