The Effects of Skewness for Insurance Ratemaking

Abstract

In Risk Theory only the actuarial risk is considered; the description of the actuarial risk is the probability distribution of the claims. On this basis an insurer’s necessary premium for covering the risk is derived. Financial models intend to develop lair” market rates of return and thus a normative price for a risky investment, or any asset in general. A fair insurance premium is derived following the idea that the fair rate of return when covering a risk by means of an insurance contract should be the same as the fair rate of return from any other risky investment. The most applied financial models are the Capital Asset Pricing Model (CAPM), the Arbitrage Pricing Model (APM) and the Option Pricing Model (OPM); for all these models a competitive market or, at least, market equilibrium is assumed, and there is no financial model which can be applied for any arbitrary probability distribution without suppressing substantial information being included in a probability distribution. The Capital Asset Pricing Model (CAPM), for instance, is based on a (µ,σ)-model, which means: Every asset or investment is regarded only in respect to µ, the expected rate of return, and a, its standard deviation. Every other information about a probability distribution is neglected; in Option Pricing Theory solutions are only considered on the basis of very special assumptions about the probability distributions.