Optimal Parlay Wagering and Whitrow Asymptotics: A State-Price and Implicit-Cash Treatment

Battle Count: 67

While the paper is specifically about betting/wagering, the mathematical framework (Kelly criterion, log-utility optimization, state-price interpretation, portfolio factorization, and asymptotic analysis of restricted menus) has direct parallels to quantitative trading. The outer-product factorization result is analogous to independent-asset portfolio construction. The singles-only restriction analysis parallels the study of transaction costs or menu restrictions in trading. The perturbative approach to understanding portfolio interaction effects is relevant to multi-asset allocation. However, the paper does not directly address financial markets, trading strategies, or risk management in the traditional sense.

The exact parlay formula (Theorem 3.1) is straightforward to implement: solve each event independently, then take the outer product. The perturbative Whitrow asymptotics (Theorem 4.2) require computing the isolated Kelly solutions, the matrices C_j and vectors a_j, and the interaction coefficients Lambda_j. The binary check (Section 6) is trivially implementable. The main complexity lies in the theoretical derivation rather than numerical implementation. For practical use, one needs to estimate state prices and probabilities accurately.

The paper is purely theoretical with complete proofs provided. All formulas, propositions, and theorems are self-contained with explicit derivations. The binary check against Thorp (Section 6) provides a verifiable special case. However, there is no code or numerical implementation provided. Reproducibility depends on the reader's ability to verify the KKT conditions and perturbative expansions analytically.