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OPTIMAL DECISIONS UNDER RECURSIVE UTILITY
by
Harun Aydilek
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(APPLIED MATHEMATICS)
August 2008
Copyright 2008 Harun Aydilek
Object Description
| Title | Optimal decisions under recursive utility |
| Author | Aydilek, Harun |
| Author email | aydilek@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2008-05-21 |
| Date submitted | 2008 |
| Restricted until | Restricted until 1 July 2010. |
| Date published | 2010-07-01 |
| Advisor (committee chair) | Zhang, Jianfeng |
| Advisor (committee member) |
Zapatero, Fernando Ma, Jin |
| Abstract | Recursive utility functions control the investors relative risk aversion (RRA) and elasticity of intertemporal substitution (EIS) by different parameters. They are generalization of expected utility functions in which the RRA and the EIS are controlled by the same parameter. This is widely discussed in the empirical literature. Also, the timing of the resolution of uncertainty matters in recursive setting. Recursive utility functions are widely used in the literature in order to explain many macroeconomic issues like the equity premium puzzle, risk free rate puzzle, and stock market participation. We want to have a deep understanding about the effects and relations of the model parameters. We use the Epstein-Zin preferences on a binomial tree and find the analytical closed form solution for the optimal allocations in consumption, risk free and risky assets. We give numerical results for the effects of model parameters. Numerical results show that the dependence of consumption on RRA parameter is insignificant. Then, we extend our model by adding lifetime uncertainty. We check the interchangeability of EIS parameter, and the subjective time discount factor under different cases like incomplete markets and stochastic lifetime. Analytically, these two parameters are not interchangeable, but numerically they are under certain lifetime, complete and incomplete markets. However, accuracy is much smaller for the uncertain lifetime model. Then, we analyze the welfare loss of suboptimal allocations. Wefind that effect of suboptimal allocation in bond holdings is insignificant. The welfare loss is larger when the suboptimal allocation is in stock holdings and consumption, but it is still modest. Finally, we numerically show that a representative agent exists when the heterogeneity is in RRA or EIS parameter. However, this is not true when the heterogeneity is in subjective time discount factor or survival probability. |
| Keyword | recursive utility; welfare loss |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m1307 |
| Rights | Aydilek, Harun |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Aydilek-20080701 |
| Archival file | uscthesesreloadpub_Volume26/etd-Aydilek-20080701.pdf |
Description
| Title | Page 1 |
| Full text | OPTIMAL DECISIONS UNDER RECURSIVE UTILITY by Harun Aydilek A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (APPLIED MATHEMATICS) August 2008 Copyright 2008 Harun Aydilek |
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