Finance and Stochastics

, Volume 4, Issue 1, pp 1–33 | Cite as

Risk sensitive asset management with transaction costs

  • Tomasz R. Bielecki
  • Stanley R. Pliska


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.

Key words: Risk-sensitive impulsive stochastic control, quasi-variational inequalities, optimal portfolio selection, incomplete markets, transaction costs 
JEL Classification: G11 
Mathematics Subject Classification (1991): 90A09, 93E20, 49N25 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Tomasz R. Bielecki
    • 1
  • Stanley R. Pliska
    • 2
  1. 1.Department of Mathematics, The Northeastern Illinois University, 5500 North St. Louis Avenue, Chicago, IL 60625-4699, USA (e-mail: US
  2. 2.Department of Finance, University of Illinois at Chicago, 601 S. Morgan St., Chicago, IL 60607-7124, USA (e-mail: US

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