A Bernoulli Utility and the St. Petersburg Paradox

As discussed in Chapter 2, the literature on risk and decision theory is deeply rooted in mathematics and economics. The study of risk is the study of chance and choice. Probability theory is the formalism to study chance and decision theory is the formalism to study choice. Their union provides the formalism to study risk.

The importance of combining the study of chance and the study of choice was recognized by Swiss mathematician Daniel Bernoulli (1700–1782) in his 1738 essay “Exposition of a New Theory on the Measurement of Risk.” In that essay, Bernoulli recognized that taking a risk is a choice to gamble on an event whose outcome is uncertain. However, a favorable or unfavorable outcome ...

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