On transformations of actuarial valuation principles

In this paper, we determine optimal trading strategies associated with the financial variance and standard deviation principles proposed by Schweizer [2001. Insurance: Mathematics and Economics 28, 31–47]. These principles take into consideration the possibilities of hedging on the financial market and are derived by an indifference argument, which embeds the traditional (actuarial) variance and standard deviation principles in a financial framework. We also investigate an alternative way of transforming actuarial principles and show that for the standard deviation principle this leads to the financial standard deviation principle. The principles are applied for the valuation and hedging of unit-linked life insurance contracts.