The Ruin Probability Of Some Risk Model Under The Erv Class

Ruin theory is the core of risk theory. Recently, the ruin theory research has developed extremely fast, and the calculation of ruin probability is considered to be the key question. There are more and more studies of them in our country. This paper analyzes and generalizes kinds of models under ERV heavy-tailed distributions, and the mixed and negatively associated ruin models after light-tailed distributions are discussed.Firstly, the background of this thesis is introduced and he basic theories about heavy-tailed distributions,negatively associated random variables and random process. Then we solve the ruin probability of number dependent models.Secondly, the ruin probability of the catastrophe insurance companies are considered. Under the ERV heavy-tailed distributions, the paper constructed a unitary negative associated risk model of fixed interest rate, by constructing compound renewal process, using the properties of ERV heavy-tailed and negative associated random variables, solve the ruin probability. Then improving multiple model, using additivity of ERV heavy-tailed, solve the ruin probability of the model by constructing compound renewal process.Finally, this paper discussed the bankruptcy probability of the insurance company both underwriting catastrophe risk and small risk. And constructed the mixed negatively associated multiple risk model with fixed interest rate under the family of ERV, proved the sum of random variables of ERV heavy-tailed distributions and Light-tailed distributions also subjected to the ERV heavy-tailed distributions. Next, the paper constructed the irregular compound renewal process, and obtained the asymptotic ruin probability of the model under the properties of ERV heavy-tailed and negatively associated random variables. Then promoted the mixed negatively associated multiple risk model to the negatively associated risk model that closer to the actual situation. Using the additivity of ERV heavy-tailed subclasses, the paper constructed the complex update process and obtained the asymptotic ruin probability of risk model.