This research is aimed at finding closed-form solutions of the utility maximization problem that solves an infinitely-lived rational consumer when the risky asset is driven by a time-inhomogeneous Markov modulated diffusion process. We provide analytical solutions for two specific cases: transition probabilities with tendency and transition probabilities with no tendency and no periodicity.
The Hurst coefficient and the alpha-stable parameter are useful indicators in the analysis of time series to detect normality and absence of self-similarity. In particular, when these two features met simultaneously the series is driven by white noise. This paper is aimed at developing an index to measure the degree to which a time series departs from white noise. The proposed index is built by using the principal component analysis of the Mahalanobis distances between the Hurst coefficient and the alpha-stable parameter from theoretical values of normality and absence of self-similarity. The proposed index is applied to examine the Mexican Peso exchange rate against the US Dollar. The distinctive characteristic of the index is that it can be used as an early warning indicator of crises, as it is shown for the Mexican case.
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