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Keywords:
Bayesian decisions; power divergences; Cox--Ross--Rubinstein binomial asset price models
Bayesian decisions; power divergences; Cox--Ross--Rubinstein binomial asset price models
Summary:
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.
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