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5906概率困难数值题long

How Many Bets Until Loss Is Unlikely

题目

A Kelly bettor on an even-money coin with p=0.6p=0.6 stakes the optimal fraction f=0.2f^*=0.2 each round. The per-round log-return is +ln1.2+\ln 1.2 with probability 0.60.6 and ln0.8\ln 0.8 with probability 0.40.4, with mean G0.0201G\approx0.0201 and variance v0.0395v\approx0.0395. Using Chebyshev's inequality, find a number of rounds nn after which the probability of ending below the starting wealth is at most 5%5\%.

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