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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2017: 0.96

SCImago Journal Rank (SJR) 2017: 0.455
Source Normalized Impact per Paper (SNIP) 2017: 0.853

Mathematical Citation Quotient (MCQ) 2017: 0.32

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Volume 35, Issue 1-2


Portfolio optimization under dynamic risk constraints: Continuous vs. discrete time trading

Imke Redeker
  • Institute of Mathematics, Brandenburg University of Technology Cottbus–Senftenberg,Postbox 101344, 03013 Cottbus, Germany
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  • Other articles by this author:
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/ Ralf Wunderlich
  • Corresponding author
  • Institute of Mathematics, Brandenburg University of TechnologyCottbus–Senftenberg, Postbox 101344, 03013 Cottbus, Germany
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-08-17 | DOI: https://doi.org/10.1515/strm-2017-0001


We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. We then investigate time discretization effects and find that the loss of portfolio performance resulting from imposing a risk constraint is typically bigger than the loss resulting from infrequent trading.

Keywords: Consumption-investment problem; stochastic optimal control; dynamic risk measure; Markov decision problem; discrete-time approximation

MSC 2010: 91G10; 93E20; 91G80


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About the article

Received: 2017-01-14

Revised: 2017-07-23

Accepted: 2017-07-31

Published Online: 2017-08-17

Published in Print: 2018-01-01

Citation Information: Statistics & Risk Modeling, Volume 35, Issue 1-2, Pages 1–21, ISSN (Online) 2196-7040, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1515/strm-2017-0001.

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