Necessary and Sufficient Conditions in the Problem of Optimal Investment in Incomplete Markets
Following Ann. Appl. Probab. 9 (1999) 904-950 we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In the previous p...
| Veröffentlicht in: | The Annals of Applied Probability. - Institute of Mathematical Statistics. - 13(2003), 4, Seite 1504-1516 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2003
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| Zugriff auf das übergeordnete Werk: | The Annals of Applied Probability |
| Schlagworte: | Primary 90A09 Secondary 90C26 Utility maximization Incomplete markets Legendre transformation Duality theory Mathematics Economics Philosophy |
| Zusammenfassung: | Following Ann. Appl. Probab. 9 (1999) 904-950 we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to find minimal conditions on a model and a utility function for the validity of several key assertions of the theory to hold true. In the previous paper we proved that a minimal condition on the utility function alone, that is, a minimal market independent condition, is that the asymptotic elasticity of the utility function is strictly less than 1. In this paper we show that a necessary and sufficient condition on both, the utility function and the model, is that the value function of the dual problem is finite. |
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| ISSN: | 10505164 |