{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:27:45Z","timestamp":1787239665257,"version":"build-2736575974"},"reference-count":5,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[1993,12]]},"abstract":"<jats:p>Consider a homogeneous Markov chain taking values in $\\{ 0,1, \\ldots ,N,N + 1\\} $, where states 0 and $N + 1$ are absorbing and the probability of absorption at state 0 prior to state $N + 1$, called the ruin probability, is of interest. It is shown that if the Markov chain is skip-free, then a simple bisection search can be applied to find the ruin probabilities. This procedure is numerically stable and considerably simpler than the matrix inversion and iteration method counterparts.<\/jats:p>","DOI":"10.1137\/1035138","type":"journal-article","created":{"date-parts":[[2005,3,7]],"date-time":"2005-03-07T02:32:15Z","timestamp":1110162735000},"page":"621-624","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Calculation of Ruin Probabilities for Skip-Free Markov Chains"],"prefix":"10.1137","volume":"35","author":[{"given":"Masaaki","family":"Kijima","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,12]]},"reference":[{"key":"R1","volume-title":"An introduction to probability theory and its applications. Vol. I","author":"Feller William","year":"1957"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6200-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1966-0199892-8"},{"key":"R4","volume-title":"Finite Markov chains","author":"Kemeny John G.","year":"1960"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.2307\/3214761"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/1035138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:44:26Z","timestamp":1787237066000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/1035138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,12]]}},"alternative-id":["10.1137\/1035138"],"URL":"https:\/\/doi.org\/10.1137\/1035138","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,12]]}}}