This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.
Nothing is so unpredictable as a throw of the dice, and yet every man who plays often will at some time or other make a Venus-cast: now and then he indeed will make it twice and even thrice in succession. Are we going to be so feebleminded then as to aver that such a thing happened by the personal intervention of Venus rather than by pure luck?
In no other branch of mathematics is it so easy for experts to blunder as in probability theory.
Statistics were magic like this: they could tell you with near-certainty that a thing would occur, without a hint of when or where.
Skill is a function of chance. It’s an intuitive best-use of chance situations.
Random chance is not sufficient to explain random chance. ~Jubal Harshaw
While in theory randomness is an intrinsic property, in practice, randomness is incomplete information.
Probability is not about the odds, but about the belief in the existence of an alternative outcome, cause, or motive.
This equation of the impersonal plus time plus chance producing the total configuration of the universe and all that is in it, modern people hold by faith.
Alan White and I spent the next two or three years working together on this. We developed what is known a stochastic volatility model. This is a model where the volatility as well as the underlying asset price moves around in an unpredictable way.
At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate.
If each of your time steps is one week long, you are not modeling the stock price terribly well over a one-week time period, because you are saying that there are only two possible outcomes.
