7 papers
The Expiring Coupon Collector: Sliding-Window Surjection Flux and Rare-Entry Laws
Christopher D. Long
We study the coupon collector with deterministic expiration: one coupon is drawn at each time, and each coupon remains active for exactly draws. Completion occurs when all …
Terminal Defects, Growing Multiplicity, and Variance Extremality in the Double Dixie Cup Problem
Christopher D. Long
We develop a terminal-defect method for the double Dixie cup problem and use it to prove the finite-variance extremality conjecture of Doumas and Papanicolaou. For every \(m\ge1\)…
Exact Finite-Horizon Quantile Kelly for Repeated Multi-Outcome Events
Christopher D. Long
We formulate and prove an exact finite-horizon quantile theorem for repeated identical multi-outcome Kelly wagering in wealth-profile / Arrow--Debreu coordinates. For a fixed -o…
Risk-Constrained Kelly for Mutually Exclusive Outcomes: CRRA Support Invariance and Logarithmic One-Dimensional Calibration
Christopher D. Long
We study the finite mutually exclusive outcome version of risk-constrained Kelly optimization with explicit state prices. The market has outcome probabilities , state prices…
Optimal Parlay Wagering and Whitrow Asymptotics: A State-Price and Implicit-Cash Treatment
Christopher D. Long
For independent multi-outcome events under multiplicative parlay pricing, we give a short exact proof of the optimal Kelly strategy using the implicit-cash viewpoint. The proof is…
Utility-Invariant Support Selection and Eventwise Decoupling for Simultaneous Independent Multi-Outcome Bets
Christopher D. Long
For simultaneous independent events with finitely many outcomes, consider the expected-utility problem with nonnegative wagers and an endogenous cash position. We prove a short sup…