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: Shapiro 1990 documented some of the criteria used by actuaries when selecting the assumptions for actuarial valuations. He noted, however, that many of these criteria are often were in conflict with one another. This paper uses expected utility theory to model this process of choosing actuarial assumption when faced with potentially conflicting criteria. The three criteria considered are prudence, best estimate and conservativeness.