From actuarial to financial valuation principles

A valuation principle is a mapping that assigns a number (value) to a rando m variable (payoff). This paper constructs a transformation on valuation pr inciples by embedding them in a financial environment. Given an a priori va luation rule u, we define the associated a posteriori valuation rule h by a n indifference argument: The u-value of optimally investing in the financia l market alone should equal the u-value of first selling the payoff at its h-value and then choosing an optimal investment strategy inclusive of the p ayoff. In an L-2-framework, we explicitly construct in this way the financi al transforms of the variance principle and the standard deviation principl e. (C) 2001 Elsevier Science B.V. All rights reserved.