Jackpotting and the survival of the worthless: Extreme-value dominance in speculative valuation

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, jackpotting : probability enters valuation sublinearly as p 1 / α , where α > 1 indexes tail sensitivity, so that assets with vastly different success probabilities command similar prices if jackpot magnitudes are comparable. Second, the survival of the worthless : assets with negligible expected value persist because valuation decays as t − 1 / α while beliefs decay as t − 1 , yielding survival times that scale as ( J / V min ) α . Both results are exact for the power-moment family V α ( X ) = ( E [ X α ] ) 1 / α 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.