This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

A Control Approach to Robust Utility Maximization with Logarithmic Utility and Time-Consistent Penalties

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Daniel Hernandez–Hernandez
Alexander Schied

Additional information is available for the following registered author(s):

Abstract

We propose a stochastic control approach to the dynamic maximization of robust utility functionals that are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an external stochastic factor process. In particular, the market model is incomplete. Our main results give conditions on the minimal penalty function of the robust utility functional under which the value function of our problem can be identified with the unique classical solution of a quasilinear PDE within a class of functions satisfying certain growth conditions. The fact that we obtain classical solutions rather than viscosity solutions is important for the use of numerical algorithms, whose applicability is demonstrated in examples.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-061.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-061.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 26 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2006-061

Contact details of provider:
Postal: Spandauer Str. 1,10178 Berlin
Phone: +49-30-2093-5708
Fax: +49-30-2093-5617
Email:
Web page: http://sfb649.wiwi.hu-berlin.de
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Janine Tellinger).

Related research
Keywords: Optimal investment; model uncertainty; incomplete markets; stochastic volatility; coherent risk measure; convex risk measure; optimal control; convex duality;

Other versions of this item:

Find related papers by JEL classification:
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Daniel Hernandez–Hernandez & Alexander Schied, 2005. "Robust Utility Maximization in a Stochastic Factor Model," SFB 649 Discussion Papers SFB649DP2006-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006. [Downloadable!]
  2. Alexander Schied & Ching-Tang Wu, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers SFB649DP2005-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Sep 2005. [Downloadable!]
  3. Lars Peter Hansen & Thomas J. Sargent, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May. [Downloadable!] (restricted)
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  5. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2007. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Working Papers halshs-00176606_v1, HAL. [Downloadable!]
    Other versions:
  6. Alexander Schied, 2005. "Optimal Investments for Risk- and Ambiguity-Averse Preferences: A Duality Approach," SFB 649 Discussion Papers SFB649DP2005-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006. [Downloadable!]
    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Christian Stoltenberg, 2006. "Real Balance Effects, Timing and Equilibrium Determination," SFB 649 Discussion Papers SFB649DP2006-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Dirk Temme & Henning Kreis & Lutz Hildebrandt, 2006. "PLS Path Modeling – A Software Review," SFB 649 Discussion Papers SFB649DP2006-084, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  3. Matthias Paustian & Christian Stoltenberg, 2006. "Optimal Interest Rate Stabilization in a Basic Sticky-Price Model," SFB 649 Discussion Papers SFB649DP2006-072, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  4. Zdenek Hlavka & Michal Pesta, 2006. "Constrained General Regression in Pseudo-Sobolev Spaces with Application to Option Pricing," SFB 649 Discussion Papers SFB649DP2006-069, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  5. Szymon Borak & Wolfgang Härdle & Stefan Trück & Rafal Weron, 2006. "Convenience Yields for CO2 Emission Allowance Futures Contracts," SFB 649 Discussion Papers SFB649DP2006-076, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  6. Jenny Kragl & Julia Schmid, 2006. "Relational Contracts and Inequity Aversion," SFB 649 Discussion Papers SFB649DP2006-085, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  7. Alexander Schied, 2007. "Robust Optimal Control for a Consumption-investment Problem," SFB 649 Discussion Papers SFB649DP2007-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. Tim Grebe & Julia Schmid & Andreas Stiehler, 2006. "Do Individuals Recognize Cascade Behavior of Others? - An Experimental Study -," SFB 649 Discussion Papers SFB649DP2006-079, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  9. Dirk Temme & Lutz Hildebrandt, 2006. "Formative Measurement Models in Covariance Structure Analysis: Specification and Identification," SFB 649 Discussion Papers SFB649DP2006-083, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  10. Enzo Giacomini & Wolfgang Härdle & Ekaterina Ignatieva & Vladimir Spokoiny, 2006. "Inhomogeneous Dependency Modelling with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2006-075, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  11. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  12. Ying Chen & Wolfgang Härdle & Vladimir Spokoiny, 2006. "GHICA - Risk Analysis with GH Distributions and Independent Components," SFB 649 Discussion Papers SFB649DP2006-078, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  13. Carsten Trenkler & Pentti Saikkonen & Helmut Lütkepohl, 2006. "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break," SFB 649 Discussion Papers SFB649DP2006-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  14. Daniel Hernández-Hernández & Alexander Schied, 2007. "Robust Maximization of Consumption with Logarithmic Utility," SFB 649 Discussion Papers SFB649DP2007-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
Statistics
Access and download statistics

Did you know? You too can volunteer for RePEc, for example by encouraging others to use our services.

This page was last updated on 2009-12-3.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.