On the Two-Times Differentiability of the Value Functions in the Problem of Optimal Investment in Incomplete Markets
We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the solutions to these problems with respect to their initial values....
Veröffentlicht in: | The Annals of Applied Probability. - Institute of Mathematical Statistics. - 16(2006), 3, Seite 1352-1384 |
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Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
2006
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Zugriff auf das übergeordnete Werk: | The Annals of Applied Probability |
Schlagworte: | Utility maximization Incomplete markets Legendre transformation Duality theory Risk aversion Risk tolerance Mathematics Economics Business Philosophy |
Zusammenfassung: | We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the solutions to these problems with respect to their initial values. We show that the key conditions for the results to hold true are that the relative risk aversion coefficient of the utility function is uniformly bounded away from zero and infinity, and that the prices of traded securities are sigma-bounded under the numéraire given by the optimal wealth process. |
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ISSN: | 10505164 |