From actuarial to financial valuation principles

A valuation principle is a mapping that assigns a number (value) to a random variable (payoff). This paper constructs a transformation on valuation principles by embedding them in a financial environment. Given an a priori valuation rule u, we define the associated a posteriori valuation rule h by an indifference argument: The u-value of optimally investing in the financial 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 payoff. In an L2-framework, we explicitly construct in this way the financial transforms of the variance principle and the standard deviation principle.