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DC Field | Value | Language |
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dc.contributor.author | Hoyle, E | - |
dc.contributor.author | Hughston, LP | - |
dc.contributor.author | Macrina, A | - |
dc.contributor.editor | Palczewski, A | - |
dc.contributor.editor | Stettner, L | - |
dc.date.accessioned | 2016-04-07T09:37:32Z | - |
dc.date.available | 2015 | - |
dc.date.available | 2016-04-07T09:37:32Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Banach Center Publications, 104, 2015, pp. 95 - 120 | en_US |
dc.identifier.isbn | 978-83-86806-27-0 | - |
dc.identifier.issn | 0137-6934 | - |
dc.identifier.uri | https://www.impan.pl/pl/wydawnictwa/banach-center-publications/all/104//86465/stable-1-2-bridges-and-insurance | - |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/12460 | - |
dc.identifier.uri | https://arxiv.org/abs/1005.0496v5 | - |
dc.description.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. | en_US |
dc.format.extent | 95 - 120 | - |
dc.language.iso | en | en_US |
dc.publisher | Polskiej Akademii Nauk, Instytut Matematyczny | en_US |
dc.subject | non-life reserving | en_US |
dc.subject | claims development | en_US |
dc.subject | reinsurance | en_US |
dc.subject | best estimate of ultimate loss | en_US |
dc.subject | information-based asset pricing | en_US |
dc.subject | Lévy processes | en_US |
dc.subject | stable processes | en_US |
dc.title | Stable-1/2 bridges and insurance | en_US |
dc.type | Article | en_US |
dc.identifier.doi | https://doi.org/10.4064/bc104-0-5 | - |
dc.relation.isPartOf | Advances in Mathematics of Finance | - |
pubs.notes | 2010 Mathematics Subject Classification: 60G52, 62P05, 62F15, 91B25, 91B30. | - |
pubs.notes | 2010 Mathematics Subject Classification: 60G52, 62P05, 62F15, 91B25, 91B30. | - |
dc.identifier.eissn | 1730-6299 | - |
Appears in Collections: | Dept of Mathematics Research Papers |
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Fulltext.pdf | 406.88 kB | Adobe PDF | View/Open |
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