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Permanent link (DOI): https://doi.org/10.7939/R3CT29

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Minimal Hellinger Deflators and HARA Forward Utilities with Applications: Hedging with Variable Horizon Open Access

Descriptions

Other title
Subject/Keyword
minimal hellinger deflator
forward utility
optimal stochastic control
random horizon
HARA forward utility
optimal portfolio
optimal sale problem
minimal hellinger martingale density
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Ma, Junfeng
Supervisor and department
Tahir Choulli (Math and Stats Sciences)
Examining committee member and department
Valentina Galvani (Economics)
Byron Schmuland (Math and Stats Sciences)
Yuri Kabanov (Mathematics, U.F.R. des Sciences et Technologie)
Edit Gombay (Math and Stats Sciences)
Tahir Choulli (Math and Stats Sciences)
Alexander Melnikov (Math and Stats Sciences)
Christoph Frei (Math and Stats Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematical Finance
Date accepted
2013-04-30T15:27:54Z
Graduation date
2013-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
This thesis develops three major essays on the topic of horizon-dependence for optimal portfolio. The first essay contributes extensively to the newest concept of forward utilities. In this essay, we describe explicitly three classes of forward utilities--that we call HARA forward utilities--as well as their corresponding optimal portfolios. The stochastic tool behind our analysis lies in the concept of Minimal Hellinger Martingale densities (called MHM densities hereafter), introduced and developed recently by Choulli and his collaborators. The obtained results for HARA forward utilities by using MHM densities are derived under assumptions on the market model. The relaxation of some of these assumptions leads to introduce the new concept of Minimal Hellinger Deflator in order to characterize HARA forward utilities. The second essay addresses the problem of finding horizon-unbiased optimal portfolio from the perspective of contract theory. In fact, we consider an agent with classical exponential utility and describe--as explicit as possible--the payoff process for which there exists a horizon-unbiased optimal hedging portfolio. The last essay focuses on the financial problem that we call optimal sale problem. This problem consists of an agent who is investing in stocks and possesses a non-tradable asset that she aims to sell. The goal of this investor is to find the optimal portfolio--from her investment in stock market--and optimal time to liquidate all her assets (tradable or not).
Language
English
DOI
doi:10.7939/R3CT29
Rights
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.
Citation for previous publication
Choulli, T., Ma, J. and Morlais, M., Three essays on exponential hedging with variable exit times, in Musiela Festschrift (Editors: Kabanov, Rutkowski and Zariphopoulou), Springer, 2012.

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