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Risks 2018, 6(3), 76; https://doi.org/10.3390/risks6030076

A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures

1
Institut für Mathematik, RWTH Aachen University, 52062 Aachen, Germany
2
Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA
*
Author to whom correspondence should be addressed.
Received: 29 June 2018 / Revised: 1 August 2018 / Accepted: 2 August 2018 / Published: 7 August 2018
(This article belongs to the Special Issue Computational Methods for Risk Management in Economics and Finance)
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Abstract

The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu (2018), presented in Part I of this series. As an alternative to classical portfolio risk measures such as the standard deviation, we, in particular, construct risk measures related to the “current” drawdown of the portfolio equity. In contrast to references Chekhlov, Uryasev, and Zabarankin (2003, 2005), Goldberg and Mahmoud (2017), and Zabarankin, Pavlikov, and Uryasev (2014), who used the absolute drawdown, our risk measure is based on the relative drawdown process. Combined with the results of Part I, Maier-Paape and Zhu (2018), this allows us to calculate efficient portfolios based on a drawdown risk measure constraint. View Full-Text
Keywords: admissible convex risk measures; current drawdown; efficient frontier; portfolio theory; fractional Kelly allocation, growth optimal portfolio; financial mathematics admissible convex risk measures; current drawdown; efficient frontier; portfolio theory; fractional Kelly allocation, growth optimal portfolio; financial mathematics
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Maier-Paape, S.; Zhu, Q.J. A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures. Risks 2018, 6, 76.

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