On the financial value of information

Results of Kelly and Breiman relating optimal growth rates for gambling and investing to information distances are generalised to include return distributions for virtually any type of game or asset. These results are achieved by first introducing the notion of the optimal financial derivative instrument for a given gamble or investment and then solving the related optimisation problem. For assets varying continuously over time, a formula for optimal dynamic portfolio adjustment follows for commonly occurring models, assuming no transaction costs. The latter results are applied to assets with normal and lognormal returns. The results for these are demonstrated using simulation.