The Ruin Probability Of Double-type Insurance Poisson Risk Model And Its Generalized Risk Model

Ruin theory is the main content of the risk theory in the insurance mathematicsresearch category, and the ruin probability stands the important place in ruin theory. It isone of the important quantitative index evaluation of the ability for insurance company.Therefore, how to proceed the effective regulation for insurance company, initiate thescientifically predicting of future premium income and claim and estimating the ruinprobability of insurance companies, are all very important subjects in insurancemathematics.There are more than one hundred study for ruin probability of insurance companyand got a lot of almost prefect results. With the rapid economical development, theinsurance industry turns more regularization and enlargement. People treat the insuranceindustry more deeply and thoroughly in knowledge and understanding. So there aremore and more requirements for the diversification of risks, single insurance risk modelhas its limits of risk regulation process. According to this requirement that wegeneralized the single insurance risk model to double-type insurance risk model, furtherenrich the research of risk model in theory. The following main of the work have donefor this thesis.There are four chapters this paper. In the first chapter, it briefly introduces thestudy background and classic Poisson risk model. In the second chapter, it involvessome concepts and method mentioned in the whole paper. In the third chapter, it studiesdouble-type insurance generalized compound Poisson risk model, and then it derivesexplicit expressions of ruin probability under the condition that the initial capitalis u and claims obey exponential distribution and combination of several exponentialdistribution. In the forth chapter, it studies double-type insurance double Poisson riskmodel. First, adjustment coefficient is proved as existent and single value with the wayof property about functions. Second, get the ruin probabilities by using the martingaleways. Third, it derives expressions of ruin probability under the condition that claimsobey exponential distribution and combination of several exponential distribution.