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Portfolio Optimization with Risk Constraints in the View of Stochastic Interest Rates

  • We discuss the portfolio selection problem of an investor/portfolio manager in an arbitrage-free financial market where a money market account, coupon bonds and a stock are traded continuously. We allow for stochastic interest rates and in particular consider one and two-factor Vasicek models for the instantaneous short rates. In both cases we consider a complete and an incomplete market setting by adding a suitable number of bonds. The goal of an investor is to find a portfolio which maximizes expected utility from terminal wealth under budget and present expected short-fall (PESF) risk constraints. We analyze this portfolio optimization problem in both complete and incomplete financial markets in three different cases: (a) when the PESF risk is minimum, (b) when the PESF risk is between minimum and maximum and (c) without risk constraints. (a) corresponds to the portfolio insurer problem, in (b) the risk constraint is binding, i.e., it is satisfied with equality, and (c) corresponds to the unconstrained Merton investment. In all cases we find the optimal terminal wealth and portfolio process using the martingale method and Malliavin calculus respectively. In particular we solve in the incomplete market settings the dual problem explicitly. We compare the optimal terminal wealth in the cases mentioned using numerical examples. Without risk constraints, we further compare the investment strategies for complete and incomplete market numerically.

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Author:William Ntambara
URN (permanent link):urn:nbn:de:hbz:386-kluedo-46020
Advisor:Joern Sass
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2017/02/28
Date of first Publication:2017/02/28
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2016/03/10
Date of the Publication (Server):2017/03/01
Number of page:X, 157
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)