Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The Grossman and Zhou investment strategy is not always optimal

Klass, M J and Nowicki, Krzysztof LU (2005) In Statistics and Probability Letters 74(3). p.245-252
Abstract
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.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
optimal asset allocation, drawdown, portfolio insurance
in
Statistics and Probability Letters
volume
74
issue
3
pages
245 - 252
publisher
Elsevier
external identifiers
  • wos:000231899600003
  • scopus:23944473379
ISSN
0167-7152
DOI
10.1016/j.spl.2005.04.060
language
English
LU publication?
yes
id
37b108be-d2da-4ec8-a331-1b0c7cb46310 (old id 223851)
date added to LUP
2016-04-01 15:46:54
date last changed
2025-10-14 11:26:00
@article{37b108be-d2da-4ec8-a331-1b0c7cb46310,
  abstract     = {{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 &lt;= t'&lt;= t) F(t')e(r(t-t')), where 0 &lt;=lambda &lt;= 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.}},
  author       = {{Klass, M J and Nowicki, Krzysztof}},
  issn         = {{0167-7152}},
  keywords     = {{optimal asset allocation; drawdown; portfolio insurance}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{245--252}},
  publisher    = {{Elsevier}},
  series       = {{Statistics and Probability Letters}},
  title        = {{The Grossman and Zhou investment strategy is not always optimal}},
  url          = {{http://dx.doi.org/10.1016/j.spl.2005.04.060}},
  doi          = {{10.1016/j.spl.2005.04.060}},
  volume       = {{74}},
  year         = {{2005}},
}