Sleeping Kelly

Battle Count: 50

The paper is directly relevant to quantitative trading through its treatment of the Kelly criterion for sequential betting and the critical distinction between expected value maximization and geometric growth rate maximization. The PGM coin flip example illustrates why maximizing expected value can lead to ruin in sequential (compounding) scenarios, which is a fundamental concern in position sizing and portfolio management. The Dutch Book analysis connects to market-making and arbitrage considerations. However, the paper is primarily a theoretical/philosophical contribution to decision theory rather than a practical trading strategy paper. The core insight—that sequential wealth dynamics require logarithmic (Kelly) optimization rather than linear expected value optimization—is foundational to quantitative position sizing.

The paper is purely theoretical with no computational implementation required. The mathematical derivations involve basic calculus (partial derivatives for optimization), algebraic manipulation of inequalities, and elementary probability. The Kelly criterion formula and wealth multiplier calculations are straightforward. No code, simulations, or complex algorithms are needed to verify the results.

Fully theoretical paper with complete mathematical derivations. All proofs (Theorem 1 and Theorem 2) are self-contained with explicit algebraic steps. The PGM coin flip example is fully worked out. No empirical data or code required. All assumptions are explicitly stated. The evaluation tables provided in the extract summarize all key results.