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5899概率困难数值题long

Betting Kelly on the Wrong Probability

题目

An even-money coin truly wins with probability p=0.55p=0.55, but you overestimate it as p^=0.65\hat p=0.65 and bet the Kelly fraction implied by your estimate. What is your actual long-run expected log-growth rate per round? Compare it to the growth you would have earned betting the correct Kelly fraction, and state what the sign of your actual growth implies.

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你的答案

actual_growth_rate

correct_kelly_growth

actual_growth_sign