On the History of the Growth-Optimal Portfolio

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 certain to outperform any other significantly different strategy as the time horizon increases. This property, in particular, has fascinated many researchers in finance and mathematics and has created a huge and exciting literature on growth-optimal investment. This chapter 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 seems to be an area where some misconceptions exist. The survey also provides an extensive review of the recent use of the GOP as a pricing tool, in, for example, 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 becomes a supermartingale.