Abstract
This paper considers the optimal selection of portfolios for utility maximizing investors under a shortfall risk constraint for a financial market model with partial information on the drift parameter. It is known that without risk constraint the distribution of the optimal terminal wealth often is quite skew. In spite of its maximum expected utility there are high probabilities for values of the terminal wealth falling short a prescribed benchmark. This is an undesirable and unacceptable property e.g. from the viewpoint of a pension fund manager. While imposing a strict restriction to portfolio values above a benchmark leads to considerable decrease in the portfolio’s expected utility, it seems to be reasonable to allow shortfall and to restrict only some shortfall risk measure.
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
Basak S, Shapiro A (2001) Value-at-risk based risk management: Optimal policies and asset prices. The Review of Financial Studies 14: 371–405
Elliott RJ (1993) New finite-dimensional filters and smoothers for noisily observed Markov chains. IEEE Transactions on Information Theory 39: 265–271
Gabih A, Grecksch W, Wunderlich R (2005) Dynamic portfolio optimization with bounded shortfall risks. Stochastic Analysis and Applications 23: 579–594
Gabih A, Grecksch W, Richter M, Wunderlich R (2006) Optimal portfolio strategies benchmarking the stock market. Mathematical Methods of Operations Research, to appear
Gabih A, Sass J, Wunderlich R (2006) Utility maximization under bounded expected loss. RICAM report 2006-24
Gandy R (2005) Portfolio optimization with risk constraints. PhD-Dissertation, Universität Ulm
Gundel A, Weber S (2005) Utility maximization under a shortfall risk constraint. Preprint
Hahn M, Putschögl W, Sass J (2006) Portfolio Optimization with Non-Constant Volatility and Partial Information. Brazilian Journal of Probability and Statistics, to appear
Haussmann U, Sass J (2004) Optimal terminal wealth under partial information for HMM stock returns. In: G. Yin and Q. Zhang (eds.): Mathematics of Finance: Proceedings of an AMS-IMS-SIAM Summer Conference June 22–26, 2003, Utah, AMS Contemporary Mathematics 351: 171–185
Karatzas I, Ocone DL, and Li J (1991) An extension of Clark’s formula. Stochastics and Stochastics Reports 37: 127–131
Lakner P, Nygren LM (2006) Portfolio optimization with downside constraints. Mathematical Finance 16: 283–299
Rieder U, Bäuerle N (2005) Portfolio optimization with unobservable Markov-modulated drift process. J. Appl. Prob. 43: 362–378
Sass J, Haussmann UG (2004) Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain. Finance and Stochastics 8: 553–577
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
Wunderlich, R., Sass, J., Gabih, A. (2007). Optimal Portfolios Under Bounded Shortfall Risk and Partial Information. In: Waldmann, KH., Stocker, U.M. (eds) Operations Research Proceedings 2006. Operations Research Proceedings, vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69995-8_92
Download citation
DOI: https://doi.org/10.1007/978-3-540-69995-8_92
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69994-1
Online ISBN: 978-3-540-69995-8
eBook Packages: Business and EconomicsBusiness and Management (R0)