Utility-Invariant Support Selection and Eventwise Decoupling for Simultaneous Independent Multi-Outcome Bets

Battle Count: 74

The paper is primarily about pari-mutuel betting and Kelly-type portfolio optimization rather than financial markets directly. However, the structural insights—utility-invariant support selection, eventwise decoupling, state-price geometry, and the threshold identity (1-P)/(1-Q)—have conceptual parallels in portfolio construction, multi-asset allocation, and risk budgeting. The independence assumption and the betting-market framing limit direct applicability to quantitative trading, but the mathematical machinery (Kuhn-Tucker decomposition, continuation factors, prefix support) is transferable to constrained portfolio optimization problems.

The theoretical result is straightforward to implement: sort outcomes within each event by edge ratio r_ℓi = p_ℓi/π_ℓi, then greedily include outcomes while the next edge ratio exceeds the threshold (1-P)/(1-Q). The support selection is O(n log n) per event and fully decoupled. Computing active weights requires solving a scalar equation for the multiplier λ (explicit for CRRA utility). The main complexity lies in the theoretical understanding, not the implementation.

The paper is entirely self-contained with complete formal proofs of all propositions, theorems, and corollaries. All definitions, assumptions, and derivations are explicitly stated. No computational experiments or external data are required. The mathematical arguments can be independently verified from the text alone.