Axiomatic Utility Theory under Risk: Non-Archimedean Representations and Application to Insurance Economics

The first attempts to develop a utility theory for choice situations under risk were undertaken by Cramer (1728) and Bernoulli (1738). Considering the famous St. Petersburg Paradox! — a lottery with an infinite expected monetary value —Bernoulli (1738, p. 209) observed that most people would not spend a significant amount of money to engage in that gamble. To account for this observation, Bernoulli (1738, pp. 199—201) proposed that the expected monetary value has to be replaced by the expec...