Some aspects of information theory in gambling and economics

Abstract

We discuss applications of information theory to the fields of gambling and economics, such as the problem of gambling on horse races with causal side information, and process of portfolio selection in the stock market. One of the center points is the gambling strategy proposed by Kelly, that, on the one hand, gave a real-life situation of a communication channel without optimum coding in which the rate of transmission is significant. On the other hand, its optimization process opened the door for the theory of rebalanced portfolios with known underlying distributions. We also overview the work on universal portfolios with and without side information, which yield portfolio strategies that have the same exponential rate of growths as the ones achieved by the best state-constant and constant rebalanced portfolios chosen after the stock outcomes are revealed. We do not intend to be encyclopedic, the topics included are bounded to reflect our own research interest. © 2013 Springer-Verlag Berlin Heidelberg.