Utility functions and decisions under uncertainty

Question

Define a utility function and describe the roles it plays in financial decision making.

Short answer

A utility function $U(W)$ assigns satisfaction to wealth, and rational agents choose to maximise expected utility. Concavity encodes risk aversion: the certainty equivalent of a gamble is below its expected value, and the curvature $-U''/U'$ measures absolute risk aversion. Common choices are exponential, power and log utility; they are used for portfolio choice, indifference pricing in incomplete markets and equilibrium asset pricing.

Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 19, p.90; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Mean-Variance Optimisation

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