An evaluation of fuzzy transportation underwriting systematic risk

From the insurance financial pricing point of view, we investigate the fuzzy transportation underwriting systematic risk made by major lines of transportation, including the insurances of automobile damage, automobile liability, compulsory automobile liability, compulsory motorcycle liability, marine hull, marine cargo, fishing vessel and aviation, in which the parameters of membership function may be the symmetric or asymmetric triangular fuzzy numbers. Our results show that the best-fitting parameters of the model from a company data are the asymmetric triangular fuzzy numbers in transportation underwriting systematic risk. We determinate the lower and upper limits of the fuzzy transportation underwriting systematic risk associated to these fuzzy numbers and show that the underwriting of most lines are below normal market risk in Taiwan, except that of the compulsory automobile liability. We also estimate the underwriting beta value for the transportation various lines and show that they may be positive or negative. It also sees that the transportation underwriting systematic risk in the fuzzy environment is larger than that in the crisp environment. Especially, we have found the ranking with best-fitting of skew factors and used them to evaluate the underwriting risk in each line, which may help us to perform the forecasting of the underwriting systematic risk and underwriting profit margin in transportation lines and to determine the appropriateness of the resulting premiums. While the investigations are the special properties of our input data of Taiwan the prescription of this paper could be apply to the transportation lines of other countries.