Study On Ruin Problem For Poisson-geometric Risk Modeli

Ruin theory has been the basis and core of modern actuarial theory and one of difficult and hot issues in actuarial research nowadays.While the ruin probability and the duration of negative surplus are a very important research direction in this subject.The former mainly focuses on the possibility for the ruin of insurance company and the latter does how to character the duration of negative surplus after the insurance company is ruined.The paper applies martingale theory and Markov theory to study ruin probability,the deficit distribution and the duration of negative surplus of the ruin problem for two types compound Poisson-Ge-ometric risk model,The main work of the paper as follows:(1)Using the strong Markov property of the surplus process,the author studies the ruin p-robability,the deficit distribution and the duration of negative surplus for a compound Poisson-Geometric process risk model under a constant interest force,an integral equation of the ruin probability and the deficit distribution,and an integral differential equation of the conditional of moment generating function for single duration of negative surplus are given.The explicit expression of the deficit distribution and the conditional moment generating function for sing-le duration of negative surplus arc obtained when the claim is exponential distribution.(2)By martingale approach,the paper studies for correlated the ruin probability,the def-icit distribution and the duration of negative surplus for aggregate claims risk model with a c-ompound Poisson-Geometric process.The author derives the integral equation of the ruin pro-bability and the Cramer-Lundberg approximation,the integral equation of the deficit distribut-ion and the moment generating function for the single duration of negative surplus and the tot-al duration of negative surplus.Finally,the author obtain the mean and variance of the total d-uration of negative surplus.The significances of the paper are as follows:Firstly,the research effectively the sub-di spersion problem of the classic risk model;Secondly,the author has considered interest rate a-nd correlated aggregate claims in the Poisson-Geometric risk model,which is beneficial to the insurance company to depict and control its real risk;Finally,it is a certain role for considering the financial warning systems of the insurance company and designing the regulatory indexes of the regulatory authority.