03251nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002000139245015600159250001700315260006300332300003100395505062900426653002401055653002001079653002001099653004001119653006401159710003401223041001901257989003801276490005601314856007201370082001001442520148501452EB000666581EBX0100000000000000051966300000000000000.0cr|||||||||||||||||||||140122 ||| eng a97836425887781 aSchmidt, Ulrich00aAxiomatic Utility Theory under RiskhElektronische RessourcebNon-Archimedean Representations and Application to Insurance Economicscby Ulrich Schmidt a1st ed. 1998 aBerlin, HeidelbergbSpringer Berlin Heidelbergc1998, 1998 aXV, 228 pbonline resource0 a1 A Survey -- 1.1 Introduction -- 1.2 The General Framework -- 1.3 Expected Utility Theory -- 1.4 Generalizations of Expected Utility -- 1.5 Conclusions -- 2 Non-Archimedean Representations -- 2.1 Introduction -- 2.2 Lexicographic Expected Utility -- 2.3 Expected Utility with Certainty Preference -- 2.4 Expected Utility on Restricted Sets -- 2.5 Conclusions -- 3 Application to Insurance Economics -- 3.1 Introduction -- 3.2 Two-Outcome Diagrams -- 3.3 Demand for Coinsurance -- 3.4 Bilateral Risk Sharing -- 3.5 Agency Theory -- 3.6 Conclusions -- References -- List of Symbols -- List of Abbreviations -- List of Figures aOperations research aDecision making aEconomic theory aOperations Research/Decision Theory aEconomic Theory/Quantitative Economics/Mathematical Methods2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aLecture Notes in Economics and Mathematical Systems uhttps://doi.org/10.1007/978-3-642-58877-8?nosfx=yxVerlag3Volltext0 a330.1 aThe 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 expected utility ("moral expectation") as the relevant criterion for decision making under risk. However, Bernoulli's 2 argument and particularly his choice of a logarithmic utility function seem to be rather arbitrary since they are based entirely on intuitively 3 appealing examples. Not until two centuries later, did von Neumann and Morgenstern (1947) prove that if the preferences of the decision maker satisfy cerĀ tain assumptions they can be represented by the expected value of a real-valued utility function defined on the set of consequences. Despite the identical mathematical form of expected utility, the theory of von Neumann and Morgenstern and Bernoulli's approach have, however, IFor comprehensive discussions of this paradox cf. Menger (1934), Samuelson (1960), (1977), Shapley (1977a), Aumann (1977), Jorland (1987), and Zabell (1987). 2Cramer (1728, p. 212), on the other hand, proposed that the utility of an amount of money is given by the square root of this amount