Appl Math Optim 39:337–360 (1999)
1999 Springer-Verlag New York Inc.
Risk-Sensitive Dynamic Asset Management
T. R. Bielecki
and S. R. Pliska
Department of Mathematics, The Northeastern Illinois University,
5500 North St. Louis Avenue, Chicago, IL 60625-4699, USA
Department of Finance, University of Illinois at Chicago,
601 S. Morgan St., Chicago, IL 60607-7124, USA
Communicated by A. Bensoussan
Abstract. 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 employmethods ofrisk-sensitive controltheory,thereby usingan 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 shownto be the solution of a partial differentialequation. 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.
KeyWords. Risk-sensitive stochastic control, Optimal portfolioselection, Incom-
plete markets, Large deviations.
AMS Classiﬁcation. Primary 90A09, Secondary 60H30, 60G35, 93E20.