Tracking a financial benchmark using a few assets

David D. Yao, Shuzhong Zhang, Xun Yu Zhou

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We study the problem of tracking a financial benchmark - a continuously compounded growth rate or a stock market index - by 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.

Original languageEnglish (US)
Pages (from-to)232-246
Number of pages15
JournalOperations research
Issue number2
StatePublished - Mar 2006


  • Semidefinite programming
  • Stabilizability
  • Steady growth-rate tracking
  • Stochastic linear quadratic control
  • Stock-index tracking


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