{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:35:53Z","timestamp":1767108953959,"version":"3.37.3"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Mulungushi University"},{"DOI":"10.13039\/501100010483","name":"Nelson Mandela African Institution of Science and Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100010483","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Zambian Ministry of Higher Education"},{"DOI":"10.13039\/100004424","name":"African Development Bank Group","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100004424","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>We consider an insurance company whose reserves dynamics follow a diffusion-perturbed risk model. To reduce its risk, the company chooses to reinsure using proportional or excess-of-loss reinsurance. Using the Hamilton-Jacobi-Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation (VIDE) which we transform into a linear Volterra integral equation (VIE) of the second kind. We then proceed to solve this linear VIE numerically using the block-by-block method for the optimal reinsurance policy that minimizes the ultimate ruin probability for the chosen parameters. Numerical examples with both light- and heavy-tailed distributions are given. The results show that proportional reinsurance increases the survival of the company in both light- and heavy-tailed distributions for the Cram\u00e9r-Lundberg and diffusion-perturbed models.<\/jats:p>","DOI":"10.1155\/2018\/9180780","type":"journal-article","created":{"date-parts":[[2018,2,22]],"date-time":"2018-02-22T23:33:37Z","timestamp":1519342417000},"page":"1-11","source":"Crossref","is-referenced-by-count":3,"title":["On Minimizing the Ultimate Ruin Probability of an Insurer by Reinsurance"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5285-0846","authenticated-orcid":true,"given":"Christian","family":"Kasumo","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Computational Science, Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juma","family":"Kasozi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry","family":"Kuznetsov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computational Science, Nelson Mandela African Institution of Science and Technology, P.O. 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