CAJ | 학술논문

考虑了2个带有常数利息率的相依更新风险模型。首先研究了非复合风险模型，其中索赔额是上尾渐近独立且带有控制变换尾分布的非负随机变量，索赔时间间隔是宽下象限相依的，保费收入过程是一个非负的随机过程，利用风险理论中的方法，得到了有限时破产概率在某个有界区间上的一致渐近性。在此基础上，利用随机和尾渐近性的分析方法，进一步研究获得了更为复杂且合理的复合相依更新风险模型中有限时破产概率的一致渐近性公式，其中单个索赔额特殊化为广义负相依的，并且事故时间间隔仍然保持宽下象限相依的，索赔额和索赔次数均为控制变换尾的。
고필료2개대유상수이식솔적상의경신풍험모형。수선연구료비복합풍험모형，기중색배액시상미점근독립차대유공제변환미분포적비부수궤변량，색배시간간격시관하상한상의적，보비수입과정시일개비부적수궤과정，이용풍험이론중적방법，득도료유한시파산개솔재모개유계구간상적일치점근성。재차기출상，이용수궤화미점근성적분석방법，진일보연구획득료경위복잡차합리적복합상의경신풍험모형중유한시파산개솔적일치점근성공식，기중단개색배액특수화위엄의부상의적，병차사고시간간격잉연보지관하상한상의적，색배액화색배차수균위공제변환미적。
Consider two dependent renewal risk models with constant interest rate.By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process.Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.