| 01-14 | Berichtsreihe des Mathematischen Seminars der Universität Kiel | |
Albrecht Irle, Jörn Saß:Portfoliooptimierung unter Transaktionskosten im Black-Scholes-Modell - ein ÜberblickPortfolio optimization is the determination of investment strategies that lead to an optimal development of the portfolio value achieving optimization within the scope of mathematically defined criteria, in particular by use of specific utility functions. In the first part of this paper we provide an overview of several problems and methods concerning portfolio optimization in the Black-Scholes model and motivate the consideration of transaction costs. In the nineties, numerous technically very elaborate papers dealing with transaction costs were published in which the transaction costs are defined in three different ways: Proportionally to volume of trade (proportional costs), proportionally to portfolio costs (fixed costs) or consisting of a constant component and proportinal costs (constant plus proportinal costs). In the second part of this paper we give a short overview of the current research and summarize the papers of Shreve and Soner (1994, proportional costs), of Morton and Pliska (1995, fixed costs) and of Korn (1998, constant plus proportinal costs).Mathematics Subject Classification (1991): 91B28 Keywords: Portfoliooptimierung, Transaktionskosten, Black-Scholes-Modell
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