Research Hub
Rigorous mathematical analysis, stochastic simulation models, and probability theory applied to Prediction Markets & Financial Derivatives Probability.
Research Pillars & Knowledge Clusters
Implied Probability & Binary Contract Pricing
Mathematical deconstruction of share prices into normalized probabilities, overround decomposition, and bookmaker margin extraction.
Cross-Market Arbitrage & Synthetic Spreads
Quantitative models for detecting pricing dislocations across prediction exchanges, dual-leg capital allocation, and slippage-adjusted risk-free execution.
Kelly Criterion & Bankroll Preservation for Binary Derivatives
Logarithmic utility maximization, fractional Kelly dampening (0.25x/0.5x), and analytical proofs on why fade strategies fail in asymmetric prediction markets.
Market Efficiency, Brier Scores & Probability Calibration
Empirical verification of market forecasting accuracy, Brier score decomposition, resolution variance, and behavioral longshot bias exploitation.
Brier score for rare events and the test a constant forecast can pass
A worked comparison on 100 synthetic outcomes shows why a small Brier score needs a reference forecast drawn from the same cases.
Implied Probability and Binary Contract Pricing: The Mathematical Foundations of Prediction Markets
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.
Cross-Market Arbitrage & Synthetic Spreads: Quantitative Mechanics of Risk-Free Prediction Strategies
Mathematical formulation of cross-venue synthetic arbitrage. Master dual-leg sizing equations, compute non-linear AMM slippage integrals, and eliminate execution oracle divergence.
Kelly Criterion for Binary Event Markets: Mathematical Derivation and the Longshot Fade Trap
Master optimal position sizing for binary derivatives. Understand the mathematical derivation of f* = (p - P_m) / (1 - P_m), deploy fractional Kelly, and see why fading longshots earns little per dollar and breaks on small errors.
Market Efficiency and Brier Score Calibration: Proper Scoring Rules and the Favorite-Longshot Bias
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.
Logarithmic Market Scoring Rules: Hanson's LMSR Cost Function & Liquidity Dynamics
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.
CPMM vs Central Limit Order Books in Prediction Derivatives: Slippage and Impermanent Loss
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.
Order Book Depth, Microstructure & Market Impact Cost in Binary Event Contracts
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.
Multi-Outcome Normalization, Dutch Book Theorems and Combinatorial Arbitrage
Mathematical principles of multi-candidate and categorical prediction markets. Deconstruct probability sum violations, Dutch book extractions, and the mechanics of Negative Risk trading.
Cross-Platform Arbitrage: Polymarket vs Kalshi Execution Calculus
Empirical and theoretical framework for cross-venue prediction market arbitrage. Model synthetic spreads between decentralized Web3 pools and CFTC-regulated institutional order books.
Synthetic Binary Replication: Sportsbook Lines and Options Digital Delta Straddles
Mathematical replication of binary prediction contracts via traditional financial options and Asian handicap sportsbooks. Construct delta-neutral hedges for macro and political volatility.
Settlement Latency, Capital Lockup Drag and Annualized Risk-Free Yield (IRR)
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.
Conditional Token Minting, Split-Merge Mechanics and Collateral Arbitrage
Explore the smart-contract collateral mechanisms of Gnosis Conditional Token Framework (CTF). Derive mathematical formulas for split-merge arbitrage, flash-minting, and pool rebalancing.
Fractional Kelly Betting: Drawdown Distribution and Volatility Boundaries
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.
Finite Horizon Risk of Ruin & Feller Absorbing Boundaries in Binary Derivatives
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.
Bankroll Growth vs Fee Drag: How Fees Change Kelly Compounding
How taker fees and commissions on profit raise the break-even probability, shrink the Kelly fraction and slow long-run growth in binary prediction markets, with the fee formulas Polymarket, Kalshi and PredictIt actually use.
Multi-Contract Portfolio Kelly Optimization with Correlation Covariance Matrices
Multivariate optimization across simultaneous prediction market positions. Model covariance structures across correlated political or financial events to avoid catastrophic portfolio drawdowns.
Whale Tracking & Copy-Trading Alpha: The Adverse Selection & Capital Inefficiency Trap
How whale tracking and copy-trading work in binary event markets, why followers face adverse selection, and what 3,236 resolved Polymarket markets show about fading longshots.
The Favourite-Longshot Bias: Overpricing Low-Probability Tail Contracts
Empirical evidence of systematic mispricing in tail prediction contracts. Contrast Kahneman-Tversky prospect theory heuristics with trading rules to exploit overpriced longshots.
Murphy's Vector Brier Score Decomposition: Step-by-Step Implementation Guide
Master the mathematical partition of probability scores into Reliability, Resolution, and Uncertainty. Step-by-step algorithms, worked matrices, and Python calibration scripts.
Logarithmic Scoring Rules, Entropy Reduction and Kullback-Leibler Divergence
Information-theoretic foundations of forecast scoring. Discover why logarithmic scoring rules strictly incentivize honest subjective probability elicitation and penalize overconfidence.
Oracle Game Theory: Schelling Points, UMA Staking and Corruption Cost Mechanics
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.
Time Decay, Volatility Compression & Terminal Dynamics in Binary Event Markets
Mathematical behavior of event contracts approaching expiration. Derive the binary Theta parameter, model Dirac delta collapse of probability variance, and avoid intraday volatility traps.
