Bayesian Decisions and Cross-Entropy Type Measures for Binomial Asset Price Models

Abstract

We study Bayesian decision making based on observations `Xn,t : t ∈ {0, Tn , 2 Tn , . . . , n Tn}´(T > 0, n ∈ N) of the discrete-time price dynamics of a financial asset, when the hypothesis a special n-period binomial model and the alternative is a different n-period binomial model. As the observation gaps tend to zero (i. e. n→∞), we obtain the limits of the corresponding Bayes risk as well as of the related Hellinger integrals and power divergences. Furthermore, we also give an example for the “non-commutativity” between Bayesian statistical and optimal investment decisions.