Optimal Investment in the Face of Adversity: Taxes, Crashes, and Illiquidity

  • This thesis deals with 3 important aspects of optimal investment in real-world financial markets: taxes, crashes, and illiquidity. An introductory chapter reviews the portfolio problem in its historical context and motivates the theme of this work: We extend the standard modelling framework to include specific real-world features and evaluate their significance. In the first chapter, we analyze the optimal portfolio problem with capital gains taxes, assuming that taxes are deferred until the end of the investment horizon. The problem is solved with the help of a modification of the classical martingale method. The second chapter is concerned with optimal asset allocation under the threat of a financial market crash. The investor takes a worst-case attitude towards the crash, so her investment objective is to be best off in the most adverse crash scenario. We first survey the existing literature on the worst-case approach to optimal investment and then present in detail the novel martingale approach to worst-case portfolio optimization. The first part of this chapter is based on joint work with Ralf Korn. In the last chapter, we investigate optimal portfolio decisions in the presence of illiquidity. Illiquidity is understood as a period in which it is impossible to trade on financial markets. We use dynamic programming techniques in combination with abstract convergence results to solve the corresponding optimal investment problem. This chapter is based on joint work with Holger Kraft and Peter Diesinger.
  • Optimales Investment unter schwierigen Bedingungen: Steuern, Crashes und Illiquidität

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Author:Frank Thomas Seifried
Advisor:Ralf Korn
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2009
Year of Publication:2009
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2009/10/12
Date of the Publication (Server):2009/10/22
Tag:Crash; Illiquidität; Portfolio-Optimierung; Worst-Case; optimales Investment
crash; illiquidity; optimal investment; portfolio optimization; tax; worst-case
GND-Keyword:Finanzmathematik; Stochastische dynamische Optimierung; Portfolio Selection; Liquidität; Steuer; Finanzkrise
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Axx Game theory / 91A15 Stochastic games
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Exx Stochastic systems and control / 93E20 Optimal stochastic control
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011