prof. PhDr. Ladislav Krištoufek, Ph.D.

Článek

10.1016/j.bir.2026.100894

Katedra aplikované matematiky

Diversification is a foundational principle in portfolio theory. Its rationale rests on the law of large numbers: aggregating independent risks reduces volatility and stabilizes outcomes. We show that this logic fails when the valuation responds disproportionately to extreme outcomes rather than to expectations. Under a tail-sensitive valuation, the combination of independent components destroys value, so that the whole is worth less than the sum of its parts. We establish this subadditivity for binary payoffs and extend it to continuous heavy-tailed distributions, showing that the result holds for any homogeneous, monotone, tail-sensitive valuation functional under mild conditions. The destruction of value by diversification increases with tail sensitivity and the number of components. Four mechanisms generate interior optima that match the observed portfolio concentration. The results of an out-of-sample exercise in cryptocurrency markets are consistent with the predicted penalty structure: random portfolios of five assets dominate the fully diversified benchmark on the tail-sensitive valuation operator in 98% of draws while matching its Sharpe ratio. The framework identifies a regime boundary that separates optimal diversification from optimal concentration environments, with the concentration premium being conditional on sufficient tail heaviness and the specific valuation regime.

Článek

10.1016/j.physa.2026.131840

Katedra aplikované matematiky

We develop a reduced-form framework for speculative valuation based on extreme-value dominance. When prices are governed by tail-sensitive functionals rather than expectations, two phenomena emerge algebraically. First, \emph{jackpotting}: probability enters valuation sublinearly as $p^{1/\alpha}$, where $\alpha > 1$ indexes tail sensitivity, so that assets with vastly different success probabilities command similar prices if jackpot magnitudes are comparable. Second, the \emph{survival of the worthless}: assets with negligible expected value persist because valuation decays as $t^{-1/\alpha}$ while beliefs decay as $t^{-1}$, yielding survival times that scale as $(J/V_{\min})^\alpha$. Both results are exact for the power-moment family $V_\alpha(X) = (\mathbb{E}[X^\alpha])^{1/\alpha}$ and qualitatively shared by related tail-responsive operators such as quantile transforms, truncated expectations, and extreme-value functionals. The framework connects speculative asset pricing to universal properties of aggregation in heavy-tailed systems without requiring equilibrium, arbitrage, or behavioural assumptions.