On the history of the Growth Optimal Portfolio Draft Version

The growth optimal portfolio (GOP) is a portfolio which has a maximal expected growth rate over any time horizon. As a consequence, this portfolio is sure to outperform any other significantly different strategy as the time horizon increases. This property in particular has fascinated many researchers in finance and mathematics created a huge and exciting literature on growth optimal investment. This paper attempts to provide a comprehensive survey of the literature and applications of the GOP. In particular, the heated debate of whether the GOP has a special place among portfolios in the asset allocation decision is reviewed as this still seem to be an area where some misconceptions exists. The survey also provides an extensive review of the recent use of the GOP as a pricing tool, in for instance the so-called “benchmark approach”. This approach builds on the numéraire property of the GOP, that is, the fact that any other asset denominated in units of the GOP become a supermartingale JEL classification: B0, G10 Mathematics Subject Classification (2000): Primary: 91B28, Secondary: 60H30, 60G44, 91B06 ∗University of Southern Denmark, Email: [email protected]. The author would like to thank Christian Riis Flor and Eckhard Platen for valuable comments and suggestions.