{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T09:51:28Z","timestamp":1777888288944,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2013,2,1]],"date-time":"2013-02-01T00:00:00Z","timestamp":1359676800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Risk and Decision Analysis"],"published-print":{"date-parts":[[2013,2]]},"abstract":"<jats:p>In this paper, we study the discounted free Gerber\u2013Shiu function for the compound binomial risk model with by-claims and randomized dividend policy. Specifically, explicit expression for the discounted free Gerber\u2013Shiu function is obtained. This result allows us to derive formulae for some useful insurance quantities, including the ruin probability, the probability function of the deficit at ruin, the joint probability function of the surplus immediately before ruin and the deficit at ruin, and the probability function of the claim causing ruin.<\/jats:p>","DOI":"10.3233\/rda-2012-0073","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T17:38:27Z","timestamp":1575394707000},"page":"3-16","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["On a discrete-time risk model with delayed claims and dividends"],"prefix":"10.1177","volume":"4","author":[{"given":"Kam Chuen","family":"Yuen","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinzhu","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rong","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2013,2]]},"container-title":["Risk and Decision Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/RDA-2012-0073","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/RDA-2012-0073","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T04:41:57Z","timestamp":1777610517000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/RDA-2012-0073"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["10.3233\/RDA-2012-0073"],"URL":"https:\/\/doi.org\/10.3233\/rda-2012-0073","relation":{},"ISSN":["1569-7371","1875-9173"],"issn-type":[{"value":"1569-7371","type":"print"},{"value":"1875-9173","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2]]}}}