What are some direct applications of information theory in economics theory and/or finance? Any relevant articles, surveys, or book references are appreciated (especially if they are targeted to readers unfamiliar with economics).
An example in finance is represented by credit risk modeling. In this specific application one tries to classify debtors with classification / prediction models. In other words, one is interested in knowing whether a given debtor-which is represented by a collection of features extracted from financial statements and qualitative information-will default or not, in a given horizon (usually 12 months). Classification problems are then solved using (among others) KNN (K-nearest neighbors), regression / classification trees and logistic regressions.
More modern methods are represented by SVM (support vector machines) or generalized mixed linear models (GLMM). In statistical model selection and classification tree formation it is quite common to use "optimization / model selection" criteria coming from information theory. The most known is probably the AIC (Akaike's Information Criterium). These criteria are usually defined by formulae involving Shannon's entropy, or Kullback Leibler's divergence. This latter is the Bregman divergence generated by (minus) the Shannon entropy. More general formulations can also be used.
-Stochastic portfolio theory by Dr Robert Fernholz (2002) uses Shannon's entropy measure to create functionally generated portfolios of stocks. Today, Dr Fernholz runs a Fund based on his insights into Stock Market dynamics. -IN portfolio management Constant proportion insurance (CPPI) is an algorithm of portfolio management that allows controlled behavior portfolios an a degree of capital protection. CPPI algorithm is derived from Kelly's Criterion for capital management which in turn is an application to gambling of Shannon's Information Theory.