Researching Insurable Border Of Catastrophe Risk Based On Ruin Model

In recent years, catastrophic(CAT) events frequent occurrence. From the global perspective, there were308CAT events, including150cases of natural disasters and158cases of man-made disasters, about directly economic losses amounting to$140billion, while insured losses with450billion. In recent years, large floods occur almost every year in the eastern region of our inland, serious damage to urban transport, as well as causing various degrees of damage to private property. From the global insurance industry perspective, the proportion of insured CAT risk is relatively small, about32percent in2013, in2012was about41%, in2011about31%. But the proportion of insured CAT risk in our country is far below the world average level. Facing with CAT risk insurance, the insurer will choose CAT risk coverage to prevent inadequate capital loss situation, if the insurer reduced CAT risk coverage, the insurer can largely limit the ruin probability, but the insurer premiums income will be reduced; if the insurer to expand the CAT risk coverage, insurers increase premiums, but the probability of bankruptcy is also amplified. The insurer who pursuing profit maximization while putting risk management as the primacy, expands the scope of the CAT risk coverage within a certain ruin probability, increasing the scope of business, could effective comply the optimal insurance status.The paper discusses the CAT risk of loss characteristics, and using knowledge of probability and statistics to describe it, which in insurance circles more mainstream view is that the risk managers used the Poisson distribution fitting probability of CAT risk, catastrophe risk was satisfied with Poisson counting process, reflecting the mutual independence of CAT events. Using the Poisson distribution to fit the strength parameters of the flood CAT occurred in the text. The loss extent of the CAT risk was fitted by generalized Pareto distribution(GPD), Lognormal, Gamma and Weibull distributions, using hypothesis test, we can find the flood catastrophe losses distribution was satisfied with GPD. In the course of CAT risk loss distribution fitting, when the shape parameter tends to zero, the GPD degenerates into an exponential distribution, so the distribution function approximated by an exponential function of CAT losses, easy to apply compound Poisson distribution model.About CAT risk insurability discussion, from traditional risk insurable conditions and analyzes the traditional risk insurable condition reality limitations. Compared to traditional risks, CAT risks that war, earthquakes, floods and other have greater variance of losses degree and smaller the probability of occurrence, weren’t often satisfied with the theory conditions of insurable risk, generally classified as uninsurable risk. However, with the theory and practice of modern insurance business, the traditional insurance insurable conditions become to face a challenge. Traditional insurable was on the basis of condition that the insurance market is not perfect, the financial capital market imperfections and just commercial insurance. But with the rapid development of modern insurance industry, capital markets and risk management techniques continue to improve, the CAT risk insurance also began to break open the ice, gradually entering the insurance market. Because of CAT risk specificity:Catastrophe recognition ambiguity, huge losses, low probability, etc., so the impact factors of catastrophe risk insurable border are mainly CAT risk characteristics and insurers characteristics.In the paper, there are two approaches to derive CAT risk insurable boundary. One is to determine the largest ruin probability that insurer can bear, using Lundberg inequality, giving the upper limit of ruin probability by adjustment coefficient, and take this limit as the insurer will bear the greatest probability of bankruptcy, and thus derive a insurable boundary function that three-dimensional variables, clearly reflecting the insurer initial surplus relations catastrophe risk security surcharge rate and the paid ratio. However, because the Lundberg inequality presence of condition bias, we can’t get an exact expression of ruin probability, there is a certain bias to border; Another is to use the ruin probability model, using classical risk surplus process to derive Gerber-Shiu Laplace change function, we can obtain an expression of ruin probability function. And introduce the surplus process of existing CAT risk, meaning joined the non-catastrophe earnings drift factor, re-model and derived ruin model and obtain insurable boundary function having three-dimensional variables, so, when the initial surplus, security surcharge rate and Payout percentage are satisfy with the insurable boundary function is greater than zero, then the catastrophe risk insurable, otherwise uninsurable. By insurable boundary function partial differential, we can expand CAT risk boundary.Finally, take the data of55times of the flood CAT economic losses occurred in the last10years for numerical analysis, using distribution fitting and parameter estimation, get the distribution of flood catastrophe losses satisfy the GPD, and exponential distribution approximation, get ruin probability and CAT risk insurable boundary function exact expression. So the insurer can select a reasonable risk portfolio to underwriting CAT risk in accordance with the boundary function.