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[[abstract]]Airlines are the business of transporting passengers in which the safety and risk have always been important. We use the fuzzy CAPM and fuzzy ICAPM models to investigate the underwriting systematic risk and profit margin of aviation transportation, in which the parameters of membership function are the asymmetric triangular fuzzy number. We calculate the underwriting systematic risk and profit margin of aviation and show that the value of underwriting systematic risk in both of CAPM and in ICAPM are positive and, while the underwriting profit margin of aviation is positive in CAPM it is negative in ICAPM. The results mean that there is a positive relationship between the return rate of underwriting and rate of market, and the return of P/L insurer is made on investments, not on the underwriting in the aviation insurance, which could be used to perform the forecasting of the underwriting profit margin and underwriting systematic risk. Our results show that the prediction model of underwriting risk and insurance price in the fuzzy environment with skew factor becomes more rational and elastic than that in the crisp environment

Underwriting Systematic Risk and Profit Margin in Fuzzy CAPM and ICAPM Models: The Case of Aviation Coverage