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 spe...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1998
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| Ausgabe: | 1st ed. 1998 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
461 |
| Schlagworte: | |
| Online-Zugang: | BTU01 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 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 cer 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 |
| Beschreibung: | 1 Online-Ressource (XV, 228 p) |
| ISBN: | 9783642588778 |
| DOI: | 10.1007/978-3-642-58877-8 |
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| 520 | |a 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 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 cer 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 | ||
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| spelling | Schmidt, Ulrich Verfasser aut Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics by Ulrich Schmidt 1st ed. 1998 Berlin, Heidelberg Springer Berlin Heidelberg 1998 1 Online-Ressource (XV, 228 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 461 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 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 cer 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 Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Risikotheorie (DE-588)4135592-1 gnd rswk-swf Nutzentheorie (DE-588)4131868-7 gnd rswk-swf Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nutzentheorie (DE-588)4131868-7 s Risikotheorie (DE-588)4135592-1 s Versicherungsmathematik (DE-588)4063194-1 s DE-604 Erscheint auch als Druck-Ausgabe 9783540643197 Erscheint auch als Druck-Ausgabe 9783642588785 https://doi.org/10.1007/978-3-642-58877-8 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Schmidt, Ulrich Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Risikotheorie (DE-588)4135592-1 gnd Nutzentheorie (DE-588)4131868-7 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| subject_GND | (DE-588)4135592-1 (DE-588)4131868-7 (DE-588)4063194-1 (DE-588)4113937-9 |
| title | Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics |
| title_auth | Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics |
| title_exact_search | Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics |
| title_exact_search_txtP | Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics |
| title_full | Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics by Ulrich Schmidt |
| title_fullStr | Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics by Ulrich Schmidt |
| title_full_unstemmed | Axiomatic Utility Theory under Risk Non-Archimedean Representations and Application to Insurance Economics by Ulrich Schmidt |
| title_short | Axiomatic Utility Theory under Risk |
| title_sort | axiomatic utility theory under risk non archimedean representations and application to insurance economics |
| title_sub | Non-Archimedean Representations and Application to Insurance Economics |
| topic | Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Risikotheorie (DE-588)4135592-1 gnd Nutzentheorie (DE-588)4131868-7 gnd Versicherungsmathematik (DE-588)4063194-1 gnd |
| topic_facet | Economic Theory/Quantitative Economics/Mathematical Methods Operations Research/Decision Theory Economic theory Operations research Decision making Risikotheorie Nutzentheorie Versicherungsmathematik Hochschulschrift |
| url | https://doi.org/10.1007/978-3-642-58877-8 |
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