We study Bayesian decision making based on observations $\left(X_{n,t} : t\in\{0,\frac{T}{n},2\frac{T}{n},\ldots,n\frac{T}{n}\}\right)$ ($T>0, n\in \mathbb{N}$) 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. $n \rightarrow \infty$), 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.
power divergences, Bayesian decisions, Cox-Ross-Rubinstein binomial asset price models
62C10, 94A17, 91B25