Tracking a Financial Benchmark Using a Few Assets

Authors:
David D. Yao;Shuzhong Zhang;Xun Yu Zhou
Affiliations:
Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027;Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China;Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
Venue:
Operations Research
Year:
2006

Citing 5
Cited 0

Topics in matrix analysis

Topics in matrix analysis
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Abstract

We study the problem of tracking a financial benchmarka continuously compounded growth rate or a stock market indexby dynamically managing a portfolio consisting of a small number of traded stocks in the market. In either case, we formulate the tracking problem as an instance of the stochastic linear quadratic control (SLQ), involving indefinite cost matrices. As the SLQ formulation involves a discounted objective over an infinite horizon, we first address the issue of stabilizability. We then use semidefinite programming (SDP) as a computational tool to generate the optimal feedback control. We present numerical examples involving stocks traded at the Hong Kong and New York Stock Exchanges to illustrate the various features of the model and its performance.