Inthisarticle,thejointdistributionsofseveralactuarialdiagnosticswhichareimportanttoinsurers’runningforthejump-diffusionriskprocessareexamined.Theyincludetheruintime,thetimeofthesurplusprocessleavingzeroultimately(simply,theultimatelyleaving-time),thesurplusimmediatelypriortoruin,thesupremeprofitsbeforeruin,thesupremeprofitsanddeficituntilitleaveszeroultimatelyandsoon.TheexplicitexpressionsfortheirdistributionsareobtainedmainlybythevariouspropertiesofL′evyprocess,suchasthehomogeneousstrongMarkovpropertyandthespatialhomogeneitypropertyetc,moveover,themanypropertiesforBrownianmotion.
