Empirical probability modeling, expected value verification, and open-source statistical tooling for Prediction Markets & Financial Derivatives Probability.
Independent audit of 1win vs Polymarket vs Kalshi fee drag with interactive capital preservation calculator.
Empirical 5,000-contract dataset, Murphy Brier decomposition, and open Python verification test suite.
35 foundational prediction market concepts with closed-form mathematical equations and worked examples.
Interactive mathematical calculators, probability distribution models, and algorithmic verification tools.
Rigorous mathematical analysis, stochastic simulation models, and probability theory applied to Prediction Markets & Financial Derivatives Probability.
Institutional research disclosure, stochastic simulation methodology, and cryptographic auditing by PredictionMarketMath Labs.
A rigorous mathematical exploration of binary outcome derivatives. Deconstruct share prices into objective probability distributions, understand Automated Market Maker (AMM) mechanics, and isolate operator overround.
Mathematical formulation of cross-venue synthetic arbitrage. Master dual-leg sizing equations, compute non-linear AMM slippage integrals, and eliminate execution oracle divergence.
Master optimal position sizing for binary derivatives. Understand the mathematical derivation of f* = (p - P_m) / (1 - P_m), deploy fractional Kelly, and uncover why fading low-probability longshots destroys capital.
Quantitative analysis of prediction market efficiency. Derive the Brier Score and Murphy's decomposition into Reliability, Resolution, and Uncertainty, and analyze the Favorite-Longshot Bias.
Mathematical derivation of Robin Hanson's LMSR automated market maker. Deconstruct the logarithmic cost function, softmax price equations, worst-case loss bounds, and multi-outcome state vectors.
Comparative architectural analysis of Constant Product Automated Market Makers (x * y = k) versus Central Limit Order Books (CLOB) in binary outcome contracts. Mathematical breakdown of terminal divergence.
Quantitative analysis of Level 2 market depth, bid-ask spreads, and non-linear market impact functions in binary prediction derivatives. Calculate VWAP and manage execution slippage.
Mathematical principles of multi-candidate and categorical prediction markets. Deconstruct probability sum violations, Dutch book extractions, and the mechanics of Negative Risk trading.
Empirical and theoretical framework for cross-venue prediction market arbitrage. Model synthetic spreads between decentralized Web3 pools and CFTC-regulated institutional order books.
Mathematical replication of binary prediction contracts via traditional financial options and Asian handicap sportsbooks. Construct delta-neutral hedges for macro and political volatility.
Quantify the opportunity cost of capital lockup in long-dated prediction markets. Formulate discounted present value equations, annualized IRR hurdles, and benchmark against SOFR yields.
Explore the smart-contract collateral mechanisms of Gnosis Conditional Token Framework (CTF). Derive mathematical formulas for split-merge arbitrage, flash-minting, and pool rebalancing.
Continuous Brownian motion approximation of binary bankroll compounding. Contrast Full Kelly, Half Kelly (0.5x), and Quarter Kelly (0.25x) staking to control peak-to-trough drawdowns.
Derivation of exact absorbing barrier probabilities in discrete and continuous trading horizons. Apply Feller's boundary equations to prevent account ruin during adverse variance runs.
Analytical and numerical proofs demonstrating how exchange settlement haircuts (such as Polymarket's 2% redemption fee or PredictIt's 10% tax) crush long-term geometric compounding rates.
Multivariate optimization across simultaneous prediction market positions. Model covariance structures across correlated political or financial events to avoid catastrophic portfolio drawdowns.
Empirical evidence of systematic mispricing in tail prediction contracts. Contrast Kahneman-Tversky prospect theory heuristics with trading rules to exploit overpriced longshots.
Master the mathematical partition of probability scores into Reliability, Resolution, and Uncertainty. Step-by-step algorithms, worked matrices, and Python calibration scripts.
Information-theoretic foundations of forecast scoring. Discover why logarithmic scoring rules strictly incentivize honest subjective probability elicitation and penalize overconfidence.
Game-theoretic security analysis of decentralized optimistic oracles. Evaluate the Cost of Corruption vs Profit from Corruption (CoC > PfC) bound and settlement ambiguity dispute risks.
Mathematical behavior of event contracts approaching expiration. Derive the binary Theta parameter, model Dirac delta collapse of probability variance, and avoid intraday volatility traps.