The Research Of Ruin Characteristic Quantities Of A Risk Model With Counting Process Is Compound Poisson Process

The thesis mainly research ruin characteristic quantities of risk model and Markov-modulated risk model of counting process is compound Poisson process.In the first model,we probe ruin characteristic quantities under risk model of counting process is compound Poisson process,principle of expectation premium were adopted,we assume counting process is compound Poisson process rather than Poisson process.we utilize the method of adjustment coefficient to calculate its ruin probability first,which is the same as the result under the classical risk model,and provide specific examples.Then,we utilize total probability formula to list integro-differential equation about expected penalty function.we derive Laplace transform of expected penalty function and ruin probability.In the second model,We probe ruin characteristic quantities under Markovmodulated risk model of counting process is compound Poisson process,method of constant rate charging were adopted,and the claim arrival intensity is affected by the environment.We utilize total probability formula to write integrodifferential equation about expected penalty function.We derive integro-differential equation of Laplace transform of expected penalty function.Since the external environment state has n,the integro-differential equation can be written as a matrix form,especially when n=2,we get the initial value of ruin probability in two states.