The Study Of Copula Model Based On Nonparametric Kernel Estimation

Firstly,we define the F function, combined with the characteristics of F function,the other F functions are given by the known F functions.We also set up the new method of constructing 2-Copula based on the F function, and give a way of finding F function; Then we define G function on the basis of distorted function, list the related properties of G function,and construct the distorted Copula function with given G function and the Copula function, finally, compare the correlated measures of the Copula function and the distorted Copula function.Secondly,Clayton Copula is used to establish a national real estate price fluctuation and the debtor and the guarantor's ability to repay the debt fluctuations connection function, in calculation, we use the national price index of real estates sales and the national cycle index of enterprise instead of the two cases of fluctuations, the marginal processes of two indexes's growth rate are got by non-parametric kernel density estimation, a Copula-Kernel model is built to calculate rank correlation,which shows the development of the national real estates market is good. When discuss the amount of cash recovered in nonperforming assets of commercial banks, we analysis the main influential factors on the amount of cash recovered. In order to describe very well the related structure of the various factors, we should take into account the tail dependence of each factor, so it's appropriate to use Clayton Copula function with the a good tail structure,the related structure of the two indexes's growth rate is got by Clayton Copula function,then we get an approximate formula of each quarter's cash recovery of non performing assets in the state-owned commercial banks. Finally, in condition of the stochastic interest rates, the interest force accumulation function is modeled with Vasicek process. With difference of change rates and fluctuations, we get the cumulative function of interest force and graphically describe the cumulative force of interest function of time trends. In the husband and wives'joint-life insurance, we analyze reserves for life insurance liabilities between the constant interest rate and stochastic ones based on independence assumption. In the entire discrete and continuous conditions, we get formulas of reserves for life insurance liabilities of different insurance types with Vasicek model and Copula. The different types of insurance analyze lifelong death insurance, death insurance of n years, the payment period last for h years, life-death insurance of n years, the payment period last for h years. At last, in case of lifelong death insurance under continuous condition, several numerical examples are illustrated, which demonstrate that the net premiums of stochastic interest are smaller than the tradition ones, in independent cases, different parameter values have less impact on the, but the different functions of death-power, the different results of net premium, so it's necessary to select the appropriate function death-power.