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Seems like a paradox:
kelly-optimal leverage for a continuous-time GBM with growth rate mu>0 and variance rate sigma^2 is f=mu/sigma^2, assuming risk-free rate is 0. f can be greater than 1. But for any discrete-time GBM, no matter how small the timestep, f<1 since
Seems like a paradox:
kelly-optimal leverage for a continuous-time GBM with growth rate mu>0 and variance rate sigma^2 is f=mu/sigma^2, assuming risk-free rate is 0. f can be greater than 1. But for any discrete-time GBM, no matter how small the timestep, f<1 since
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lognormal pdf goes negative otherwise. But isn't continuous-time GBM supposed to be limiting case of discrete-time GBM as timestep goes to 0?
@SinclairEuan @bennpeifert @choffstein @ole_b_peters
lognormal pdf goes negative otherwise. But isn't continuous-time GBM supposed to be limiting case of discrete-time GBM as timestep goes to 0?
@SinclairEuan @bennpeifert @choffstein @ole_b_peters
