Applied Mathematics and Optimization

, Volume 39, Issue 3, pp 337–360 | Cite as

Risk-Sensitive Dynamic Asset Management

  • T. R. Bielecki
  • S. R. Pliska


This paper develops a continuous time portfolio optimization model where the mean returns of individual securities or asset categories are explicitly affected by underlying economic factors such as dividend yields, a firm's return on equity, interest rates, and unemployment rates. In particular, the factors are Gaussian processes, and the drift coefficients for the securities are affine functions of these factors. We employ methods of risk-sensitive control theory, thereby using an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk-aversion parameter. Even with constraints on the admissible trading strategies, it is shown that the optimal trading strategy has a simple characterization in terms of the factor levels. For particular factor levels, the optimal trading positions can be obtained as the solution of a quadratic program. The optimal objective value, as a function of the risk-aversion parameter, is shown to be the solution of a partial differential equation. A simple asset allocation example, featuring a Vasicek-type interest rate which affects a stock index and also serves as a second investment opportunity, provides some additional insight about the risk-sensitive criterion in the context of dynamic asset management.

Key words. Risk-sensitive stochastic control, Optimal portfolio selection, Incomplete markets, Large deviations. AMS Classification. Primary 90A09, Secondary 60H30, 60G35, 93E20. 


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Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

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

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