I introduce Stochastic Portfolio Theory (SPT), which is an alternative approach to optimal investment, where the investor aims to beat an index instead of optimising a mean-variance or expected utility criterion. Portfolios which achieve this are called relative arbitrages, and simple and implementable types of such trading strategies have been shown to exist in very general classes of continuous semimartingale market models, with unspecified drift and volatility processes but realistic assumptions on the behaviour of stocks which come from empirical observation. I present some of my recent work on this, namely the so-called diversity-weighted portfolio with negative parameter. This portfolio outperforms the market quite significantly, for which I have found both theoretical and empirical evidence.
