Indifference pricing of insurance contracts in a product space model

The financial variance and standard deviation principles of Schweizer (2001b) are applied for the valuation of insurance contracts. These principles are financial transformations of the classical actuarial variance and standard deviation principles and take into consideration the possibilities of hedging on financial markets. We focus on the role of the information available to the insurer and study its impact on the fair premiums and the optimal trading strategies for insurance claims with financial risk. The presentation is kept within a product space model, a construction which is discussed in detail. Via a projection argument for Hilbert spaces, we show that the variance of the so-called non-hedgeable part of an insurance claim increases when the information is restricted from one filtration to a smaller filtration. By considering two extreme filtrations for the pure insurance risk, we arrive at simple upper and lower bounds for the fair premiums.