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Risk sensitive asset management with transaction costs

Author

Listed:
  • Stanley R. Pliska

    (Department of Finance, University of Illinois at Chicago, 601 S. Morgan St., Chicago, IL 60607-7124, USA Mansucript)

  • Tomasz R. Bielecki

    (Department of Mathematics, The Northeastern Illinois University, 5500 North St. Louis Avenue, Chicago, IL 60625-4699, USA)

Abstract

This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska.

Suggested Citation

  • Stanley R. Pliska & Tomasz R. Bielecki, 2000. "Risk sensitive asset management with transaction costs," Finance and Stochastics, Springer, vol. 4(1), pages 1-33.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:1:p:1-33
    Note: received: July 1998; final version received: January 1999
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    Citations

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    Cited by:

    1. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    2. Watanabe, Yûsuke, 2013. "Asymptotic analysis for a downside risk minimization problem under partial information," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1046-1082.

    More about this item

    Keywords

    Risk-sensitive impulsive stochastic control; quasi-variational inequalities; optimal portfolio selection; incomplete markets; transaction costs;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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