Competitive Portfolio Selection Using Stochastic Predictions

We study a portfolio selection problem where a player attempts to maximise a utility function that represents the growth rate of wealth. We show that, given some stochastic predictions of the asset prices in the next time step, a sublinear expected regret is attainable against an optimal greedy algorithm, subject to tradeoff against the "accuracy" of such predictions that learn (or improve) over time. We also study the effects of introducing transaction costs into the model.