Diversified Portfolios with Jumps in a Benchmark Framework

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On the Distributional Characterization of Daily Log‐Returns of a World Stock Index (2006, background): “As shown in Platen (2004b, 2005), such a diversified portfolio is robust against variations in weightings as long as the weight of each contributing stock remains reasonably small.”
Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices (2007, background): “In particular, we will further consider the following special cases: Variance Gamma: ᾱ = 0 and λ > 0, [see Madan and Semeta (1990)]; Student-t: ᾱ = 0 and λ < 0, [see Praetz (1972)]; Hyperbolic: λ = 1, [see Eberlein and Keller (1995)] and Normal Inverse Gaussian: λ = −0.”
M-6-On Minimal Market Models and Minimal Martingale Measures (2010, unknown): “Theorem 3.6 of Platen (2005) states that under fairly weak assumptions, a sequence of well-diversified portfolios converges in a suitable sense to the growth-optimal portfolio.”
Approximating the numéraire portfolio by naive diversification (2010, methodology): “The Pareto parameter α is chosen similarly to the one estimated in Simon and Bonini (1958) for the distribution of company sizes.”