Peer-reviewed studies, preprints and classic methods papers on pricing, efficiency, risk and research practice. Each entry is our summary, with the original link and a plain statement of what the study does not show.
Summaries are original paraphrases of published abstracts and records; no paper text is reproduced. Bibliographic details were checked against publisher, index and author listings on 25 October 2026. Where a paper was later corrected, the correction is shown. Preprints are labelled as not peer reviewed.
5 sources
Maximising the expected logarithm of wealth gives the fastest long-run exponential growth; with fair odds that maximum growth rate equals the channel's information rate. The staking rule derived here became known as the Kelly criterion.
Does not show: That full Kelly stakes are sensible when probabilities are estimated, or that any real betting edge exists.
When probabilities are estimated with error, Kelly stakes should be shrunk; shrunken strategies outperformed raw Kelly out of sample in their simulations and tennis illustration.
Does not show: A universal fraction of Kelly that is safe for everyone, or that the underlying tennis model had a real edge.
In simulations, risk-constrained Kelly bets achieved better trade-offs than fractional Kelly: more growth at the same drawdown risk, or less drawdown risk at the same growth.
Does not show: That drawdown constraints protect a bettor whose probability estimates are wrong.
Explains Kelly's growth properties and why many practitioners bet a fraction of Kelly to reduce volatility.
Does not show: That any particular sports-betting edge exists.
Kelly maximises long-run growth but can be very risky in the short run; fractional Kelly trades some growth for substantially lower risk.
Does not show: Which fraction suits an individual bettor.
