We study Bayesian decision making based on observations (Xn,t:t∈{0,Tn,2Tn,…,nTn}) (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.