The Top-Down Approach to Calculation of the Insurance Premium
When the risk loading for the whole portfolio is set proportionally to the standard deviation, then the problem of coherent pricing of individual risks arises. Borch (1962), proposed a solution based on Shapley's value of the n-person game. However, the solution is suited only for small n, rather reflecting the game played by few companies that negotiate pooling their portfolios. Otto (2004) proposed an intuitively appealing approximation for the case of large n that leads to allocation of the risk loading proportionaly to variances. The paper is devoted to formally justify that the variance principle can be justified as an approximation to the Shapley's solution. (original abstract)
- Borch Karl H., 1962, "Application of Game Theory to Some Problems in Automobile Insurance", ASTIN Bulletin Vol. 2, No. 2, pp. 208-221.
- Buhlmann Hans, 1985, "Premium Calculation from Top Down", ASTIN Bulletin Vol. 15, No. 2.
- Mięta Paweł, Wojciech Otto, 2005. "Premiums, Investments and Reinsurance" - Chapter 20, pp. 453-488, in: Statistical Tools for Finance and Insurance, ed. Pavel Cizek, Wolfgang Haerdle and Rafał Weron, Springer Verlag.
- Otto Wojciech, 2004, Ubezpieczenia majątkowe - Część I - Teoria ryzyka, WNT, Warsaw, Poland.
- Shapley L.S., 1953, "A value for n-person games", Annals of Mathematical Studies, Princeton, pp. 307-317.