Investment strategies and hidden variables

The present study shows how the information on `hidden' market variables effects optimal investment strategies. We take the point of view of two investors, one who has access to the hidden variables and one who only knows the quotes of a given asset. Following Kelly's theory on investment strategies, the Shannon information and the doubling investment rate are quantified for both investors. Thanks to his privileged knowledge, the first investor can follow a better investment strategy. Nevertheless, the second investor can extract some of the hidden information looking at the past history of the asset variable. Unfortunately, due to the complexity of his strategy, this investor will have computational difficulties when he tries to apply it. He will than follow a simplified strategy, based only on the average sign of the last l quotes of the asset. This results have been tested with some Monte Carlo simulations.