A Type Of Collective Risk And Studies On Ruin Probability

Risk theory is a branch of insurance actuarial science, which studies the insurer in the total compensation cost of variability, and this variability and the insurer bearing capacity and the relationship between. On the theory of the risk is mainly:Loss distribution theory; overall risk model; ruin theory and utility theory and its application. The theory of risk, ruin theory is a very important issue in, for certain types of, Putative claim number process {N(t):t≥0} that is assumed to occur at any length of h interval number of claims of the subordinate parameters for λh Poisson distribution. With the interval of the location and the information previously unrelated. Obviously, the Poisson process is a smooth, with independent increment random process. S(t) For the moment t the claim. The claim amount, and the assumption that the claim amount is independent and has the same distribution function P(x) of non negative random variables, with mean u.Consider an insurance company, define the surplus process or risk process is as follows: U(t)=u+ct-S(t),t≥0or the moment tthe insurance company earnings, u Said the insurance company’s initial assets, c unit time premium income, and c is a constant. Only by satisfying the conditions of the probability of ruin not only to1place, so called the security loading coefficient. The insurance company in actual operation, the most concern is the probability of ruin, the surplus for the first time at a certain moment is negative. The theory is that the insurance company bankrupt. Remember the time for bankruptcy. T=mf{t:t≥0andU(t)<0}If for all t≥0, There are U(t)>0, The promise T=∞, Said the insurance company does not occur in bankruptcy. In mindv Ψ(U)=Pr(T<∞),call Ψ(U)as the initial surplus is u the case of the bankruptcy probability of occurrence, referred to as the bankruptcy probability. Because the insurance company in business can encounter a variety of problems, so it is often required to probability or the model was modified and the additional condition, makes the model more close to the actual operation of insurance companies, which makes the study of ruin probability is more challenging, but the study of ruin probability has long been the focus of attention. For insurance companies, ruin probability can be used as a comprehensive insurance premium and the claim of insurance company stability of an index, risk management is a useful tool, it can be as an insurance company, a very useful early riskwarning means, so the ruin theory research also has the very important significance.Risk model is a quantitative qualitative research the effective tool of risk theory. Riskmodels include the classical risk model and modern risk model. In this paper, the risk modelof time surplus basis, gives a claim number process delay risk model--INARCR model, thestudy of its mathematical characteristics and its ruin probability problem.The first chapter mainly introduces the history and present situation of risk theory, andintroduces the main results of the classical risk model and the generalization of the classicalrisk model model.The second chapter mainly introduces the risk theory of three kinds of risk models,individual risk model, short-term collective risk model and long-term risk model, the mainresearch methods.The third chapter introduces the classical risk model in two kinds of promotion model,double Poisson two dimensional risk model and general arrival of claims risk model.The fourth chapter introduces the surplus model, surplus process, including the claimsprocess, and the ruin probability and adjustment coefficient.The fifth chapter of the INARCR risk model, including its mathematic features and ruinprobability problem.