{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T18:04:51Z","timestamp":1759514691677},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>In this paper we introduce an insurance ruin model with an adaptive premium rate, henceforth referred to as restructuring\/refraction, in which classical ruin and bankruptcy are distinguished. In this model the premium rate is increased as soon as the wealth process falls into the <jats:italic>red zone<\/jats:italic> and is brought back to its regular level when the wealth process recovers. The analysis is focused mainly on the time a refracted L\u00e9vy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from [11] and [16], we identify the distribution of various functionals related to occupation times of refracted spectrally negative L\u00e9vy processes. For example, these results are used to compute both the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring.<\/jats:p>","DOI":"10.1017\/s0021900200012043","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:11Z","timestamp":1459263071000},"page":"1171-1188","source":"Crossref","is-referenced-by-count":7,"title":["On the Time Spent in the Red by a Refracted L\u00e9vy Risk Process"],"prefix":"10.1017","volume":"51","author":[{"given":"Jean-Fran\u00e7ois","family":"Renaud","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200012043_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-012-9317-4"},{"key":"S0021900200012043_ref2","first-page":"645","volume":"41","year":"2011","journal-title":"Astin Bull"},{"key":"S0021900200012043_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s10959-013-0501-4"},{"key":"S0021900200012043_ref12","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1331216839"},{"key":"S0021900200012043_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/08-AIHP307"},{"key":"S0021900200012043_ref10","volume-title":"Gerber\u2013Shiu Risk Theory","year":"2013"},{"key":"S0021900200012043_ref9","volume-title":"Introductory Lectures on Fluctuations of L\u00e9vy Processes with Applications","year":"2006"},{"key":"S0021900200012043_ref8","first-page":"97","volume-title":"L\u00e9vy Matters II","year":"2012"},{"key":"S0021900200012043_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s13385-012-0052-6"},{"key":"S0021900200012043_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.12.044"},{"key":"S0021900200012043_ref5","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1324046014"},{"key":"S0021900200012043_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s13385-011-0006-4"},{"key":"S0021900200012043_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2013.11.005"},{"key":"S0021900200012043_ref3","doi-asserted-by":"publisher","DOI":"10.1080\/03461238.2011.624686"},{"key":"S0021900200012043_ref15","doi-asserted-by":"publisher","DOI":"10.3150\/11-BEJ404"},{"key":"S0021900200012043_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/asb.2013.4"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200012043","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:20:31Z","timestamp":1682500831000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200012043\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12]]},"references-count":16,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["S0021900200012043"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200012043","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12]]}}}