Betting Under Common Beliefs: The Effect of Probability Weighting

Battle Count: 75

The paper provides theoretical foundations for understanding why speculative trade (betting) can occur even with common beliefs, which is relevant to understanding market microstructure and the existence of derivatives markets. The probability weighting framework connects to behavioral finance models used in trading. However, the paper is purely theoretical with no trading strategies, price predictions, or empirical market analysis. The relevance is indirect: it explains the existence of betting/speculation rather than providing tools for quantitative trading.

The mathematical machinery is sophisticated: quantile reformulation of comonotonic allocations, convex envelope computation for non-convex distortion functions, pointwise optimization with monotonicity constraints, and integral equations for optimal nudging. Implementing the closed-form solutions requires careful handling of the convex envelope (tangent point computation), inverse functions of marginal utility ratios, and numerical integration for certainty equivalents. The theoretical framework is elegant but requires advanced mathematical economics background to implement.

The paper provides complete mathematical proofs in the Appendix, explicit closed-form solutions under specific functional forms (CARA utility, Prelec weighting), and detailed numerical examples with parameter values. However, no code or computational scripts are provided. The theoretical framework is fully self-contained with all assumptions stated. Reproducibility requires implementing the quantile optimization and convex envelope computations independently.