Recursive Utility and Stochastic Differential Utility: From Discrete to Continuous Time
- In this thesis, mathematical research questions related to recursive utility and stochastic differential utility (SDU) are explored. First, a class of backward equations under nonlinear expectations is investigated: Existence and uniqueness of solutions are established, and the issues of stability and discrete-time approximation are addressed. It is then shown that backward equations of this class naturally appear as a continuous-time limit in the context of recursive utility with nonlinear expectations. Then, the Epstein-Zin parametrization of SDU is studied. The focus is on specifications with both relative risk aversion and elasitcity of intertemporal substitution greater that one. A concave utility functional is constructed and a utility gradient inequality is established. Finally, consumption-portfolio problems with recursive preferences and unspanned risk are investigated. The investor's optimal strategies are characterized by a specific semilinear partial differential equation. The solution of this equation is constructed by a fixed point argument, and a corresponding efficient and accurate method to calculate optimal strategies numerically is given.
Verfasser*innenangaben: | Thomas Seiferling |
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URN: | urn:nbn:de:hbz:386-kluedo-43808 |
Betreuer*in: | Frank Thomas Seifried |
Dokumentart: | Dissertation |
Sprache der Veröffentlichung: | Englisch |
Datum der Veröffentlichung (online): | 22.05.2016 |
Jahr der Erstveröffentlichung: | 2016 |
Veröffentlichende Institution: | Technische Universität Kaiserslautern |
Titel verleihende Institution: | Technische Universität Kaiserslautern |
Datum der Annahme der Abschlussarbeit: | 28.04.2016 |
Datum der Publikation (Server): | 23.05.2016 |
Seitenzahl: | XI, 207 |
Fachbereiche / Organisatorische Einheiten: | Kaiserslautern - Fachbereich Mathematik |
DDC-Sachgruppen: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Lizenz (Deutsch): | Standard gemäß KLUEDO-Leitlinien vom 30.07.2015 |