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The Grossman and Zhou investment strategy is not always optimal

Publiceringsår: 2005
Språk: Engelska
Sidor: 245-252
Publikation/Tidskrift/Serie: Statistics and Probability Letters
Volym: 74
Nummer: 3
Dokumenttyp: Artikel i tidskrift
Förlag: Elsevier


Grossman and Zhou [1993. Optimal investment strategies for controlling drawdowns. Math. Finance 3, 241-276] proposed a strategy to maximize the asymptotic long-run growth rate of one's fortune F, subject to its never falling below lambda sup(0 <= t'<= t) F(t')e(r(t-t')), where 0 <=lambda <= 1 is a fixed constant chosen by the investor and r is a fixed, known, non-negative, continuously compounded interest rate on invested capital. In this paper we show that the strategy proposed in Grossman and Zhou does not retain its optimal long-run growth property when generalized to the discrete-time setting.


  • Probability Theory and Statistics
  • optimal asset allocation
  • drawdown
  • portfolio insurance


  • ISSN: 0167-7152

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