On the financial value of information

Results of Kelly [5] and Breiman [2] relating optimal growth rates for gamb ling and investing to information distances are generalised to include retu rn distribution?; for virtually any type of game or asset. These results ar e achieved by first introducing the notion of the optimal financial derivat ive instrument for a given gamble or investment and then solving the relate d optimisation problem. For assets varying continuously over time. a formul a fur optimal dynamic portfolio adjustment follows for commonly occurring m odels, assuming no transaction costs. The latter results are applied to ass ets with normal and lognormal returns. The results for these are demonstrat ed using simulation.