On a robust parameter-free pricing principle: Fair value and risk adjusted premium.

This paper was prepared for the 1st International IAA Life Colloquium (June 10-13, 2007, Stockholm, Sweden).

For the space of all feasible risks with arbitrary mean and standard deviation and a fixed limit, the use of the rule of thumb "actuarial premium = mean + half of standard deviation" is justified. It is shown that this actuarial premium coincides with the maximum of the minimum risk adjusted premium obtained from a simple solvency model under the assumption that the supervising authority chooses the minimum level of "fair" actuarial premium and values the insolvency risk with the risk-neutral distortion risk measure. A case study using dynamic Monte Carlo simulation of the balance sheet of a portfolio of endowment life insurance shows that the introduced profit loading absorbs in average the random claims fluctuations.