湖北大学学报（自然科学版）
湖北大學學報（自然科學版）
호북대학학보（자연과학판）
2015年
3期
208-212
,共5页
多险种多复合Poisson-Geometric风险模型%生存概率%积分-微分方程%利率%Laplace变换
多險種多複閤Poisson-Geometric風險模型%生存概率%積分-微分方程%利率%Laplace變換
다험충다복합Poisson-Geometric풍험모형%생존개솔%적분-미분방정%리솔%Laplace변환
multi-compound Poisson-Geometric risk model of multi-type-insurance%survival probability%integral-differential equation%interest rate%Laplace transforms
建立多险种多复合Poisson-Geometric过程的常利率风险模型，得到该模型的生存概率所满足的积分-微分方程.当无保费收入时，由所得到的积分-微分方程推出生存概率的Laplace变换的表达式，对于初始盈余为0时，得到生存概率的精确解.并给出具体的数值计算的实例以解释我们的结果.①
建立多險種多複閤Poisson-Geometric過程的常利率風險模型，得到該模型的生存概率所滿足的積分-微分方程.噹無保費收入時，由所得到的積分-微分方程推齣生存概率的Laplace變換的錶達式，對于初始盈餘為0時，得到生存概率的精確解.併給齣具體的數值計算的實例以解釋我們的結果.①
건립다험충다복합Poisson-Geometric과정적상리솔풍험모형，득도해모형적생존개솔소만족적적분-미분방정.당무보비수입시，유소득도적적분-미분방정추출생존개솔적Laplace변환적표체식，대우초시영여위0시，득도생존개솔적정학해.병급출구체적수치계산적실례이해석아문적결과.①
A multi-compound Poisson-Geometric risk model of multi-type-insurance with a constant interest rate was constructed,and the integral-differential equation of the survival probability under this model was derived.Using the integral-differential equation we established,we got the explicit expression about the Laplace transforms of the survival probability and the exact solution was given when the initial surplus was zero and there were no premium incomes. Finally,we gave a numerical example to illustrate our results.
