A note on optimal portfolios under regime-switching

This paper extends the stochastic dominance rules for normal mixture distributions derived by Levy and Kaplanski (2015). First, the portfolios under consideration are allowed to follow different regime-switching processes. Second, the results are extended from second- to fourth-order stochastic dominance, which is known to be closely related to kurtosis aversion in financial markets and allows to compare mixture distributions with the same overall variance. In particular, when a risk-free asset is available, checking for fourth-order stochastic dominance turns out to amount to a comparison of the regime-specific and overall Sharpe ratios of the portfolios under consideration.