Description: We apply decision theory to develop a credibility formula that minimizes a loss function that is a linear combination of a squared-error term and a second-derivative term. The squared-error term measures the accuracy of the estimator, while the second-derivative term constrains the estimator to be close to linear.

Description: In this paper, the authors take an axiomatic approach to characterize insurance prices in a competitive market setting. Four axioms are presented to describe the behavior of market insurance prices. From these axioms it follows that the price of an insurance risk has a Choquet integral representation with respect to a distorted probability.