In a complete financial market model, the price of a contingent claim is determined by arbitrage arguments, without involving the preferences of economic agents. In an incomplete model, such claims may carry an intrinsic risk which cannot be hedged away. In order to determine desirable strategies in view of such risks, the preferences of an investor should be made explicit, and this is often done in terms of an expected utility criterion.

The paradigm of expected utility is the theme of this chapter. We begin with a general discussion of preference relations on a set X of alternative choices and their numerical representation by some functional U on X . In the financial context, such choices can usually be described as payoff profiles. ...

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