{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T08:40:53Z","timestamp":1682498453165},"reference-count":5,"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":"<jats:p>The Asmussen\u2013Kroese Monte Carlo estimators of P(<jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>n<\/jats:italic>\n               <\/jats:sub> &amp;gt; <jats:italic>u<\/jats:italic>) and P(<jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>N<\/jats:italic>\n               <\/jats:sub> &amp;gt; <jats:italic>u<\/jats:italic>) are known to work well in rare event settings, where <jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>N<\/jats:italic>\n               <\/jats:sub> is the sum of independent, identically distributed heavy-tailed random variables <jats:italic>X<\/jats:italic>\n               <jats:sub>1<\/jats:sub>,\u2026,<jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>N<\/jats:italic>\n               <\/jats:sub> and <jats:italic>N<\/jats:italic> is a nonnegative, integer-valued random variable independent of the <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>i<\/jats:italic>\n               <\/jats:sub>. In this paper we show how to improve the Asmussen\u2013Kroese estimators of both probabilities when the <jats:italic>X<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>i<\/jats:italic>\n               <\/jats:sub> are nonnegative. We also apply our ideas to estimate the quantity E[(<jats:italic>S<\/jats:italic>\n               <jats:sub>\n                  <jats:italic>N<\/jats:italic>\n               <\/jats:sub>-<jats:italic>u<\/jats:italic>)<jats:sub>+<\/jats:sub>].<\/jats:p>","DOI":"10.1017\/s0021900200012961","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:49:29Z","timestamp":1459262969000},"page":"1188-1193","source":"Crossref","is-referenced-by-count":2,"title":["Improving the Asmussen\u2013Kroese-Type Simulation Estimators"],"prefix":"10.1017","volume":"49","author":[{"given":"Samim","family":"Ghamami","sequence":"first","affiliation":[]},{"given":"Sheldon M.","family":"Ross","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S0021900200012961_ref3","volume-title":"Monte Carlo Methods in Financial Engineering","year":"2004"},{"key":"S0021900200012961_ref2","volume-title":"Modelling Extremal Events","year":"1997"},{"key":"S0021900200012961_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s11857-009-0088-0"},{"key":"S0021900200012961_ref5","volume-title":"Simulation","year":"2006"},{"key":"S0021900200012961_ref1","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1151337084"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900200012961","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T08:01:58Z","timestamp":1682496118000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900200012961\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":5,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["S0021900200012961"],"URL":"https:\/\/doi.org\/10.1017\/s0021900200012961","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}