Stochastic Finance, 4th Edition

2.3Expected utility

In this section, we focus on individual financial assets under the assumption that their payoff distributions at a fixed time are known, and without any regard to hedging opportunities in the context of a financial market model. Such asset distributions may be viewed as lotteries with monetary outcomes in some interval on the real line. Thus, we take M as a fixed set of Borel probability measures on a fixed interval S ⊂ ℝ. In this setting, we discuss the paradigm of expected utility in its standard form, where the function u appearing in the von Neumann–Morgenstern representation has additional properties suggested by the monetary interpretation. We introduce risk aversion and certainty equivalents, and illustrate these notions ...