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DEFLATORS, LOG-OPTIMAL PORTFOLIO AND NUMERAIRE PORTFOLIO FOR MARKETS UNDER RANDOM HORIZON
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- Author / Creator
- Yansori, Sina
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This thesis addresses two important topics of deflators and log-utility-related optimal portfolios for markets stopped at a random time T. This random time can model the death time of an agent in life insurance or the default time of a firm in credit risk. For the topic of deflators, the thesis elaborates extensively an explicit parametrization of the set of all deflators, which constitutes the dual set of all “admissible” wealth processes. We describe explicitly both cases of local martingale deflators and supermartingale delators as well.Concerning the second topic of optimal portfolios, we focus on quantifying the impact of random time on these portfolios. In fact, we consider log-utility maximization problem, whose solution relies on and is intimately related to the optimal deflators. Thus, we start by describing the optimal deflator for stopped models at random time T and then elaborate the duality which leads to the log-optimal portfolio. In meantime, as an important intermediate result, we characterize the log-optimal deflator and log-optimal portfolio for general semimartingale market models without the no-free-lunch-with-vanishing-risk assumption. Finally, the numeraire portfolio for model stopped at T is also detailed and fully described in different manners.For both topics, the thesis elaborates results for general semimartingales models and illustrates those results on several practical models. Among these, we cite the exponential Levy models (such as Jump-diffusion model and Black-Scholes market model), the volatility models (such as Corrected Stein and Stein Model and Barndorff-Nielsen Shephard Model), complete market model, and discrete time market models.
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- Graduation date
- Spring 2019
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- Type of Item
- Thesis
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- Degree
- Doctor of Philosophy
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.