Ruin Probability for Some Mixed Linear Exponential Family in Classical Risk Process

This article presents the probability of ruin for classical risk process by including density function claims which satisfies a mixed linear exponential family. can be defined as , where src=image/13428362_02.gif>, src=image/13428362_03.gif>, src=image/13428362_20.gif> is positive integer with src=image/13428362_04.gif> src=image/13428362_05.gif>, src=image/13428362_06.gif>, src=image/13428362_07.gif>, and src=image/13428362_08.gif> canonical parameter. The main results show that ordinary differential equation in general case using chain rule mathematical induction technique given Theorem 2.2, some family when src=image/13428362_09.gif>, src=image/13428362_10.gif>, src=image/13428362_11.gif>, src=image/13428362_12.gif>, src=image/13428362_13.gif>, src=image/13428362_14.gif> demonstrated 2.3, an explicit solution conditions are src=image/13428362_15.gif>, src=image/13428362_16.gif>, src=image/13428362_10.gif> src=image/13428362_17.gif>, src=image/13428362_13.gif> indicated 2.4. Finally, we use MATLAB to generate numerical simulations number Poisson gamma distribution under 2.4 parameters src=image/13428362_18.gif>=1 src=image/13428362_19.gif>=0.2. reveal relative frequency also satisfy Lundberg inequality necessary condition probability. In addition, absolute values its differences small order confirm correct.