Risk-Sensitive Dynamic Asset Management |
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Authors: | T R Bielecki S R Pliska |
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Institution: | (1) Department of Mathematics, The Northeastern Illinois University, 5500 North St. Louis Avenue, Chicago, IL 60625-4699, USA t-bielecki@neiu.edu , US;(2) Department of Finance, University of Illinois at Chicago, 601 S. Morgan St., Chicago, IL 60607-7124, USA srpliska@uic.edu , US |
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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 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.
Accepted 10 December 1997 |
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Keywords: | , Risk-sensitive stochastic control, Optimal portfolio selection, Incomplete markets, Large deviations, AMS Classification,,,,,,Primary 90A09, Secondary 60H30, 60G35, 93E20, |
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