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Ruin probabilities under general investments and heavy-tailed claims
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-9210-121X
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2011 (English)In: Finance and Stochastics, ISSN 0949-2984, E-ISSN 1432-1122, Vol. 15, no 2, 243-265 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, the asymptotic decay of finite time ruin probabilities is studied. An insurance company is considered that faces heavy-tailed claims and makes investments in risky assets whose prices evolve according to quite general semimartingales. In this setting, the ruin problem corresponds to determining hitting probabilities for the solution to a randomly perturbed stochastic integral equation. A large deviation result for the hitting probabilities is derived that holds uniformly over a family of semimartingales. This result gives the asymptotic decay of finite time ruin probabilities under sufficiently conservative investment strategies, including ruin-minimizing strategies. In particular, as long as the insurance company invests sufficiently conservatively, the investment strategy has only a moderate impact on the asymptotics of the ruin probability.

Place, publisher, year, edition, pages
2011. Vol. 15, no 2, 243-265 p.
Keyword [en]
Ruin probabilities, Heavy tails, Large deviations
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-34670DOI: 10.1007/s00780-010-0135-7ISI: 000290573800003Scopus ID: 2-s2.0-79955933889OAI: oai:DiVA.org:kth-34670DiVA: diva2:423098
Note
QC 20110614Available from: 2011-06-14 Created: 2011-06-13 Last updated: 2017-12-11Bibliographically approved

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Hult, Henrik

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