Research On Three Kinds Of Compound Risk Model Bankruptcy

Risk theory is an important branch of Probability Theory and MathematicalStatistics, also the core content of the Actuarial Mathematics. While, Bankruptcytheory is the core content of the Risk theory. In recent years, classical risk model isgeneralized by many scholars, and certain results are achieved. Further researcheshave been made on the basis of existing achievements in this paper, and the resultsinclude the following aspects:First, we have popularize the classical risk model to a discrete risk model inwhich the premium rate is a Poisson process and the number of compensation rate is abinomial process. The existence of the adjustment coefficient is proved by usingdifferential method, the ruin probability formula is derived by using the momentgenerating function method, which is consistent with the classical risk model.Second, we have popularize the premium arrival process. considering the actualsituation that the risk event and the compensation event is not necessarily equivalent,we have generalize the claim process to a compound Poison-Geometric process,introduce stochastic disturbance, and build the multi insurance risk model under theconditions of interference, extend the related results in the literature.Third, we have popularize the classical risk model to the risk model withinterference whose premium obeys the Poison process and number of claims obeysthe compound Poison-Geometric process. We not only study the ruin probabilitymodel, but also get an integral differential equation of survival probability. Theseconclusions have certain directive significance to assess the risk of insurancecompanies.