For CRRA utility with a wealth-scaled Tsallis entropy regularizer, the exploratory optimal strategy is Gaussian for entropy index 1 and Wigner semicircular for index 3, with the same mean as Merton's strategy, and can be ill-posed for p<0.
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Exploratory Utility Maximization Problem with Tsallis Entropy
For CRRA utility with a wealth-scaled Tsallis entropy regularizer, the exploratory optimal strategy is Gaussian for entropy index 1 and Wigner semicircular for index 3, with the same mean as Merton's strategy, and can be ill-posed for p<0.