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Article: Minimizing the probability of absolute ruin under ambiguity aversion

TitleMinimizing the probability of absolute ruin under ambiguity aversion
Authors
KeywordsAbsolute ruin probability
Ambiguity aversion
Mean-variance premium principle
Per-claim reinsurance
Robust optimization
Issue Date2020
PublisherSpringer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/
Citation
Applied Mathematics and Optimization, 2020, Epub 2020-09-07 How to Cite?
AbstractIn this paper, we consider an optimal robust reinsurance problem in a diffusion model for an ambiguity-averse insurer, who worries about ambiguity and aims to minimize the robust value involving the probability of absolute ruin and a penalization of model ambiguity. It is assumed that the insurer is allowed to purchase per-claim reinsurance to transfer its risk exposure, and that the reinsurance premium is computed according to the mean-variance premium principle which is a combination of the expected-value and variance premium principles. The optimal reinsurance strategy and the associated value function are derived explicitly by applying stochastic dynamic programming and by solving the corresponding boundary-value problem. We prove that there exists a unique point of inflection which relies on the penalty parameter greatly such that the robust value function is strictly concave up to the unique point of inflection and is strictly convex afterwards. It is also interesting to observe that the expression of the optimal robust reinsurance strategy is independent of the penalty parameter and coincides with the one in the benchmark case without ambiguity. Finally, some numerical examples are presented to illustrate the effect of ambiguity aversion on our optimal results.
Persistent Identifierhttp://hdl.handle.net/10722/287723
ISSN
2020 Impact Factor: 3.582
2020 SCImago Journal Rankings: 0.913
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHan, X-
dc.contributor.authorLiang, Z-
dc.contributor.authorYuen, KC-
dc.contributor.authorYuan, Y-
dc.date.accessioned2020-10-05T12:02:19Z-
dc.date.available2020-10-05T12:02:19Z-
dc.date.issued2020-
dc.identifier.citationApplied Mathematics and Optimization, 2020, Epub 2020-09-07-
dc.identifier.issn0095-4616-
dc.identifier.urihttp://hdl.handle.net/10722/287723-
dc.description.abstractIn this paper, we consider an optimal robust reinsurance problem in a diffusion model for an ambiguity-averse insurer, who worries about ambiguity and aims to minimize the robust value involving the probability of absolute ruin and a penalization of model ambiguity. It is assumed that the insurer is allowed to purchase per-claim reinsurance to transfer its risk exposure, and that the reinsurance premium is computed according to the mean-variance premium principle which is a combination of the expected-value and variance premium principles. The optimal reinsurance strategy and the associated value function are derived explicitly by applying stochastic dynamic programming and by solving the corresponding boundary-value problem. We prove that there exists a unique point of inflection which relies on the penalty parameter greatly such that the robust value function is strictly concave up to the unique point of inflection and is strictly convex afterwards. It is also interesting to observe that the expression of the optimal robust reinsurance strategy is independent of the penalty parameter and coincides with the one in the benchmark case without ambiguity. Finally, some numerical examples are presented to illustrate the effect of ambiguity aversion on our optimal results.-
dc.languageeng-
dc.publisherSpringer New York LLC. The Journal's web site is located at http://link.springer.de/link/service/journals/00245/-
dc.relation.ispartofApplied Mathematics and Optimization-
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: https://doi.org/[insert DOI]-
dc.subjectAbsolute ruin probability-
dc.subjectAmbiguity aversion-
dc.subjectMean-variance premium principle-
dc.subjectPer-claim reinsurance-
dc.subjectRobust optimization-
dc.titleMinimizing the probability of absolute ruin under ambiguity aversion-
dc.typeArticle-
dc.identifier.emailYuen, KC: kcyuen@hku.hk-
dc.identifier.authorityYuen, KC=rp00836-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s00245-020-09714-y-
dc.identifier.scopuseid_2-s2.0-85090303914-
dc.identifier.hkuros315620-
dc.identifier.volumeEpub 2020-09-07-
dc.identifier.isiWOS:000566882700001-
dc.publisher.placeUnited States-
dc.identifier.issnl0095-4616-

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