Abstract
In this paper, we study the discounted renewal aggregate claims with a full dependence structure. Based on a mixing exponential model, the dependence among the inter-claim times, the claim sizes, as well as the dependence between the inter-claim times and the claim sizes are included. The main contribution of this paper is the derivation of the closed-form expressions for the higher moments of the discounted aggregate renewal claims. Then, explicit expressions of these moments are provided for specific copulas families and some numerical illustrations are given to analyze the impact of dependency on the moments of the discounted aggregate amount of claims.
Highlights
Over the past few years, extensive studies on the risk aggregation problem for insurance portfolios have appeared in the literature
Among these studies we find Albrecher and Boxma (2004), Albrecher and Teugels (2006) and Boudreault et al (2006) which analyze ruin-related problems; Léveillé et al (2010), Léveillé and Adékambi (2011, 2012), investigate the risk aggregation and the distribution of the discounted aggregate amount of claims; Léveillé and Garrido (2001a, 2001b) use the renewal theory to derive a closed expressions for the first two moments of the discounted aggregated claims; and Léveillé and Hamel (2013) study the aggregate discount payment and expenses process for medical malpractice insurance
Closed expressions for the moments of the aggregate discounted claims are obtained when the claims and the subsequent inter-claim are distributed as Pareto and
Summary
Over the past few years, extensive studies on the risk aggregation problem for insurance portfolios have appeared in the literature. Risks 2018, 6, 86 could lead to frequent and high losses This means that in such context a positive dependence between the claim sizes and the inter-claim times should be observed. Barges et al (2011) introduce the dependence between the claim sizes and the inter-claim times using a Farlie-Gumbel-Morgenstern (FGM) copula and derive a close-from expression for the moments of the discounted aggregate claims. The main variable of interest in this paper is the discounted aggregate amount of claims up to a certain time Z (t) defined as follows. = {1, 2, · · · }} forms a sequence of continuous positive dependent and identically distributed rvs with a common cumulative distribution function (cdf) FW (.) and a survival function (sf) FW (.) = 1 − FW (.), The claim amounts { Xk , k ∈ N?
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
