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.
Author: | Thomas Seiferling |
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URN: | urn:nbn:de:hbz:386-kluedo-43808 |
Advisor: | Frank Thomas Seifried |
Document Type: | Doctoral Thesis |
Language of publication: | English |
Date of Publication (online): | 2016/05/22 |
Year of first Publication: | 2016 |
Publishing Institution: | Technische Universität Kaiserslautern |
Granting Institution: | Technische Universität Kaiserslautern |
Acceptance Date of the Thesis: | 2016/04/28 |
Date of the Publication (Server): | 2016/05/23 |
Page Number: | XI, 207 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vom 30.07.2015 |