Asymptotic Invariance of Kelly Allocation Under Power-Law Asset Dynamics: Evidence from Bitcoin

We examine log-optimal portfolio allocation when the long-run price of an asset follows a power-law trajectory, $P(t)=At^α$, and its instantaneous return variance decays as $σ^2(t)=σ_0^2 t^{-2γ}$. Under a zero risk-free-rate benchmark, the continuous-time Kelly fraction scales as $K^\ast(t)=(α/σ_0^2