Abstract
This research paper analyzes the distributional properties of stock index time series data from a new perspective, that is, time optimal decision making building on the conceptual foundation of the time optimal approach to portfolio selection introduced by Burkhardt. In this approach, the investor’s goal is to reach a predefined level of wealth as soon as possible. We investigate the empirical properties of the goal reaching times for DAX stock index investments for various levels of aspired wealth, compare the observed properties to those expected by the Inverse Gaussian distributional model, investigate the use of overlapping instead of independent goal reaching times, and highlight some methodological issues involved in the empirical analysis. The results are of immediate interest to investors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BURKHARDT, T. (1999): Time Optimal Portfolio Selection: Mean-varianceefficient Sets for Arithmetic and Geometric Brownian Price Processes. In: R. Decker and W. Gaul (Eds.): Classification and Information Processing at the Turn of The Millenium. Springer, Heidelberg, 304–311.
BURKHARDT, T. (2000a): Wachstumsorientierte Portfolioselektion auf der Grundlage von Zielerreichungszeiten. OR Spektrum, 22, 203–237.
BURKHARDT, T. (2000b) Portfolioselektion bei unsicherer Anlagedauer. Habilitationsschrift, Technische Universität Freiberg.
CHHIKARA, R.S. and FOLKS, J.L. (1989): The Inverse Gaussian Distribution — Statistical Theory, Methodology and Applications. Dekker, New York.
KAMSTRA, M. and MILEVSKY, M.A. (2005): Waiting for Returns: Using Space-Time Duality to Calibrate Financial Diffusions. Quantitative Finance 5,3, 237–244.
SCOTT, D.M. (2001): Probability Density Estimation. In: N.J. Smelser and P.B. Baltes (Eds.): International Encyclopedia of the Social and Behavioral Sciences. Pergamon, Oxford.
SILVERMAN, B.W. (1986): Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
WASAN, M.T. (1969): First Passage Time Distribution of Brownian Motion with Positive Drift (Inverse Gaussian Distribution). Queen’s Paper in Pure and Applied Mathematics, No. 19. Queen’s University, Kingston.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burkhardt, T., Haasis, M. (2007). On Goal Reaching Time Distributions Estimated from DAX Stock Index Investments. In: Decker, R., Lenz, H.J. (eds) Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70981-7_60
Download citation
DOI: https://doi.org/10.1007/978-3-540-70981-7_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70980-0
Online ISBN: 978-3-540-70981-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)