{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:41:25Z","timestamp":1682494885746},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2012,12]]},"abstract":"Consider a general bivariate L\u00e9vy-driven risk model. The surplus process Y<\/jats:italic>, starting with Y<\/jats:italic>\n 0<\/jats:sub>=x<\/jats:italic> &gt; 0, evolves according to dY<\/jats:italic>\n \n t<\/jats:italic>\n <\/jats:sub>= Y<\/jats:italic>\n \n t<\/jats:italic>-<\/jats:sub> dR<\/jats:italic>\n \n t<\/jats:italic>\n <\/jats:sub> -dP<\/jats:italic>\n \n t<\/jats:italic>\n <\/jats:sub> for t<\/jats:italic> &gt; 0, where P<\/jats:italic> and R<\/jats:italic> are two independent L\u00e9vy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P<\/jats:italic> has a L\u00e9vy measure of extended regular variation and the stochastic exponential of R<\/jats:italic> fulfills a moment condition. We obtain a simple and unified asymptotic formula as x<\/jats:italic>\u2192\u221e, which confirms Paulsen's conjecture.<\/jats:p>","DOI":"10.1017\/s0021900200012791","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:29Z","timestamp":1459262969000},"page":"939-953","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Ruin Probabilities for a Bivariate L\u00e9vy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments"],"prefix":"10.1017","volume":"49","author":[{"given":"Xuemiao","family":"Hao","sequence":"first","affiliation":[]},{"given":"Qihe","family":"Tang","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S0021900200012791_ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2008.03.004"},{"key":"S0021900200012791_ref28","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1127322015"},{"key":"S0021900200012791_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2009.12.002"},{"key":"S0021900200012791_ref19","volume-title":"Theory of Martingales","year":"1989"},{"key":"S0021900200012791_ref18","volume-title":"Introductory Lectures on Fluctuations of L\u00e9vy Processes with Applications","year":"2006"},{"key":"S0021900200012791_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6687(02)00189-0"},{"key":"S0021900200012791_ref16","doi-asserted-by":"publisher","DOI":"10.1080\/03461238.1998.10413991"},{"key":"S0021900200012791_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2007.06.002"},{"key":"S0021900200012791_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005985"},{"key":"S0021900200012791_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(01)00148-X"},{"key":"S0021900200012791_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s007800100057"},{"key":"S0021900200012791_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6687(00)00045-7"},{"key":"S0021900200012791_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(94)90113-9"},{"key":"S0021900200012791_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-010-0135-7"},{"key":"S0021900200012791_ref6","doi-asserted-by":"publisher","DOI":"10.1080\/15326340802641006"},{"key":"S0021900200012791_ref11","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1240319582"},{"key":"S0021900200012791_ref5","doi-asserted-by":"publisher","DOI":"10.1137\/1110037"},{"key":"S0021900200012791_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005205"},{"key":"S0021900200012791_ref4","volume-title":"Regular Variation","year":"1987"},{"key":"S0021900200012791_ref3","volume-title":"Ruin Probabilities","year":"2010"},{"key":"S0021900200012791_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1028903531"},{"key":"S0021900200012791_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2012.05.017"},{"key":"S0021900200012791_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2003.07.001"},{"key":"S0021900200012791_ref27","volume-title":"Stable Non-Gaussian Random Processes","year":"1994"},{"key":"S0021900200012791_ref26","doi-asserted-by":"publisher","DOI":"10.1080\/15326349108807204"},{"key":"S0021900200012791_ref25","volume-title":"Stochastic Integration and Differential Equations","year":"2005"},{"key":"S0021900200012791_ref24","doi-asserted-by":"publisher","DOI":"10.1214\/08-PS134"},{"key":"S0021900200012791_ref23","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1037125862"},{"key":"S0021900200012791_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(98)00012-X"},{"key":"S0021900200012791_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6687(98)00009-2"},{"key":"S0021900200012791_ref20","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1354716592"},{"key":"S0021900200012791_ref31","doi-asserted-by":"publisher","DOI":"10.2307\/1426858"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200012791","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T07:16:02Z","timestamp":1682493362000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200012791\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":32,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["S0021900200012791"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200012791","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}