Ruin probabilities in a Sparre Andersen model with dependency structure based on a threshold window

Eric C. K. Cheung, Suhang Dai and Weihong Ni

Annals of Actuarial Science, 2018, vol. 12, issue 2, 269-295

Abstract: We analyse ruin probabilities for an insurance risk process with a more generalised dependence structure compared to the one introduced in Constantinescu et al. (2016). In this paper, we assume that a random threshold window is generated every time after a claim occurs. By comparing the previous inter-claim time with the threshold window, the distributions of the current threshold window and the inter-arrival time are determined. Furthermore, the statuses for the previous and current inter-arrival times give rise to the current claim size distribution as well. Like Constantinescu et al. (2016), we first identify the embedded Markov additive process where all the randomness takes a general form. Inspired by the Erlangisation technique, the key message of this paper is to analyse such risk process using a Markov fluid flow model where the underlying random variables follow phase-type distributions. This would further allow us to approximate the fixed observation windows by Erlang random variables. Then ruin probabilities under the process with Erlang(n) observation windows are proved to be Erlangian approximations for those related to the process with fixed threshold windows at the limit. An exact form of the limit can be obtained whose application will be illustrated further by a numerical example.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:anacsi:v:12:y:2018:i:02:p:269-295_00

Access Statistics for this article

More articles in Annals of Actuarial Science from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().