If that's foreign to you, you might be interested in this write-up I did about election-forecasting in which I considered the same example, just in discrete time rather than continuous time:
http://nautil.us/issue/70/variables/how-to-improve-political...
The basic idea is that if you increase the volatility of a random-walk process, say by making the step-sizes larger, that won't actually make the probability of finishing above where you started any less (or more) volatile. The higher volatility means that from any given starting point your final resting place is more dispersed, but you're also more likely to range farther from home as you go. The two effects exactly cancel. Taleb's critique misses the second part of that.
If that's foreign to you, you might be interested in this write-up I did about election-forecasting in which I considered the same example, just in discrete time rather than continuous time: http://nautil.us/issue/70/variables/how-to-improve-political...
The basic idea is that if you increase the volatility of a random-walk process, say by making the step-sizes larger, that won't actually make the probability of finishing above where you started any less (or more) volatile. The higher volatility means that from any given starting point your final resting place is more dispersed, but you're also more likely to range farther from home as you go. The two effects exactly cancel. Taleb's critique misses the second part of that.