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Quantitative Finance · Glossaire

Qu'est-ce que « Fractional Kelly, drawdown, risk of ruin » ?

Aussi appelé : fractional Kelly · drawdown · risk of ruin

Definition 29.5 Markets II: Rates, FX and Credit · Chapitre 29 — Thinking in Expected Value

Fractional Kelly stakes a multiple c<1c < 1 of the Kelly fraction. A drawdown is a fall of wealth from its previous peak, measured as a fraction of that peak. The risk of ruin of a staking rule is the probability that wealth ever falls to a given fraction of its starting value.

Wealth after 300 flips of the 60% coin from USD 25 (dashed), uncapped, for four multiples of the Kelly fraction, on a log scale: the 10th, 50th and 90th percentiles of 4 000 simulated players each. Kelly has the highest median; half Kelly the best worst tenth; twice Kelly a median below the stake. Data: the chapter’s tutorial, seeded.
Figure 29.2. Wealth after 300 flips of the 60% coin from USD 25 (dashed), uncapped, for four multiples of the Kelly fraction, on a log scale: the 10th, 50th and 90th percentiles of 4 000 simulated players each. Kelly has the highest median; half Kelly the best worst tenth; twice Kelly a median below the stake. Data: the chapter’s tutorial, seeded.
Probability that wealth ever falls to half its starting value, against the multiple of Kelly staked, on a 55% even-money bet: the continuous-time formula and the share of 1 000 simulated paths of 4 000 bets. Data: the chapter’s tutorial, seeded.
Figure 29.3. Probability that wealth ever falls to half its starting value, against the multiple of Kelly staked, on a 55% even-money bet: the continuous-time formula and the share of 1 000 simulated paths of 4 000 bets. Data: the chapter’s tutorial, seeded.
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