Asymptotic Multivariate Dominance: A Financial Application

Methodology and Computing in Applied Probability - Tập 18 - Trang 1097-1115 - 2016
Sergio Ortobelli Lozza1,2, Tommaso Lando1,2, Filomena Petronio2, Tomáš Tichý2
1Department SAEQM, University of Bergamo, Bergamo, Italy
2Department of Finance, VŠB- Technical University of Ostrava, Ostrava, Czech Republic

Tóm tắt

We propose a multivariate stochastic dominance relation aimed at ranking different financial markets/sectors from the point of view of a non-satiable risk averse investor. In particular, we assume that the vector of returns of a given market is in the domain of attraction of a symmetric stable Paretian law in order to take into account the asymptotic behaviour of the financial returns. We determine the stochastic dominance rule for stable symmetric distributions, where the stability parameter plays a crucial role. Consequently, the multivariate rule for ordering markets is based on a comparison between i) location parameters, ii) dispersion parameters, and iii) stability indices. Finally, we apply the method to the equity markets of the four countries with the highest gross domestic product in 2013, namely, the US, China, Japan and Germany. In this empirical comparison we examine the ex ante and ex post dominance between stock markets, either assuming that the returns are jointly (or conditionally, for a robust approach) Gaussian distributed, or in the domain of attraction of a stable sub-Gaussian law.

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