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http://bura.brunel.ac.uk/handle/2438/12460
Title: | Stable-1/2 bridges and insurance |
Authors: | Hoyle, E Hughston, LP Macrina, A |
Keywords: | non-life reserving;claims development;reinsurance;best estimate of ultimate loss;information-based asset pricing;Lévy processes;stable processes |
Issue Date: | 2015 |
Publisher: | Polskiej Akademii Nauk, Instytut Matematyczny |
Citation: | Banach Center Publications, 104, 2015, pp. 95 - 120 |
Abstract: | We develop a class of non-life reserving models using a stable-1/2 random bridge to to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The “best-estimate ultimate loss process” is given by the conditional expectation of the ultimate loss. We derive explicit expressions for the best-estimate ultimate loss process, and for expected recoveries arising from aggregate excess-of-loss reinsurance treaties. Use of a deterministic time change allows for the matching of any initial (increasing) development pattern for the paid claims. We show that these methods are well-suited to the modelling of claims where there is a non-trivial probability of catastrophic loss. The generalized inverse-Gaussian (GIG) distribution is shown to be a natural choice for the a priori ultimate loss distribution. For particular GIG parameter choices, the best-estimate ultimate loss process can be written as a rational function of the paid-claims process. We extend the model to include a second paid-claims process, and allow the two pro- cesses to be dependent. The results obtained can be applied to the modelling of multiple lines of business or multiple origin years. The multi-dimensional model has the property that the dimensionality of calculations remains low, regardless of the number of paid-claims processes. An algorithm is provided for the simulation of the paid-claims processes. |
URI: | https://www.impan.pl/pl/wydawnictwa/banach-center-publications/all/104//86465/stable-1-2-bridges-and-insurance https://bura.brunel.ac.uk/handle/2438/12460 https://arxiv.org/abs/1005.0496v5 |
DOI: | https://doi.org/10.4064/bc104-0-5 |
ISBN: | 978-83-86806-27-0 |
ISSN: | 0137-6934 |
Appears in Collections: | Dept of Mathematics Research Papers |
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