Alex Bilzerian
RT @GoujianofYue: @alexbilz https://t.co/VfEgyQuXdp
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RT @GoujianofYue: @alexbilz https://t.co/VfEgyQuXdp
"In any profession, 90% of people are clueless but work by situational imitation, narrow mimicry & semi-conscious role-playing. Except social "science" and journalism where it is 99% and 100%, respectively."
@nntaleb tweet
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Alex Bilzerian
RT @alexbilz: 'The first principle is that you must not fool yourself—and you are the easiest person to fool.'
— Richard Feynman
https://t.co/uBISjy1o9v
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RT @alexbilz: 'The first principle is that you must not fool yourself—and you are the easiest person to fool.'
— Richard Feynman
https://t.co/uBISjy1o9v
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Alex Bilzerian
RT @RDouady: Thank you @nntaleb for raising this question of negative probabilities. As mathematicians, we often use a wording that is not necessarily intuitive and may take a meaning the goes against common sense. This is the price to pay when we need absolute rigor. Too many subtleties in the various concepts we create and not enough words (whatever the language!)
"Negative probabilities" in math or physics don't necessary mean that some event has a negative probability to occur (meaning yet to be made precise) but that we are dealing with quantities we call "probability" that happen to take negative values.
You rightfully took the examples of option prices, or broker's odds in some bets, that reflect a "market implied probability". This "implied probability', given from supply and demand, can possibly negative, meaning that either there is an arbitrage or, if we account for the bid/ask spread, that the remuneration of the market maker is lower than its theoretical value.
There are plenty of other cases where we call "probability" or "volatility" a number that can go negative. For instance, a negative volatility would imply that there are formally no solutions to Kolmogorov's diffusion equation (i.e. Black-Scholes, heat, Fokker-Planck...) But the non-existence relies on a continuous time assumption, which is not necessarily satisfied. Temporarily, we may support an unstable semi-group generator, something that likely occurs in speculative bubbles or market squeezes.
In quantum mechanics, they are related to some negative eigenvalues of operators supposed to be positive, or other issues of this kind. Many paradoxes in here, some being at the source of important phenomena, such as entanglement. The violation of Bell's inequalities, experimentally proven by Aspect, proved that Einstein was wrong in asserting "God doesn't play dice". Basically, one had a choice of accepting negative probabilities or renouncing to the locality principle. It turned out that the latter was the best explanation, and this led to quantum computing.
I also posted about our Antifragility paper, where the non-positiveness of the transfer function between Gamma and Vega can also be interpreted as some negative implied volatility, something physically realizable, which, as we discussed, can be related to Simpson paradox for the far out-of-the-money behavior of stochastic processes.
I wish that the contenders of subtle notions who claim "common sense" would better know what they are talking about and show the necessary rigor in their alleged mathematical criticism!
tweet
RT @RDouady: Thank you @nntaleb for raising this question of negative probabilities. As mathematicians, we often use a wording that is not necessarily intuitive and may take a meaning the goes against common sense. This is the price to pay when we need absolute rigor. Too many subtleties in the various concepts we create and not enough words (whatever the language!)
"Negative probabilities" in math or physics don't necessary mean that some event has a negative probability to occur (meaning yet to be made precise) but that we are dealing with quantities we call "probability" that happen to take negative values.
You rightfully took the examples of option prices, or broker's odds in some bets, that reflect a "market implied probability". This "implied probability', given from supply and demand, can possibly negative, meaning that either there is an arbitrage or, if we account for the bid/ask spread, that the remuneration of the market maker is lower than its theoretical value.
There are plenty of other cases where we call "probability" or "volatility" a number that can go negative. For instance, a negative volatility would imply that there are formally no solutions to Kolmogorov's diffusion equation (i.e. Black-Scholes, heat, Fokker-Planck...) But the non-existence relies on a continuous time assumption, which is not necessarily satisfied. Temporarily, we may support an unstable semi-group generator, something that likely occurs in speculative bubbles or market squeezes.
In quantum mechanics, they are related to some negative eigenvalues of operators supposed to be positive, or other issues of this kind. Many paradoxes in here, some being at the source of important phenomena, such as entanglement. The violation of Bell's inequalities, experimentally proven by Aspect, proved that Einstein was wrong in asserting "God doesn't play dice". Basically, one had a choice of accepting negative probabilities or renouncing to the locality principle. It turned out that the latter was the best explanation, and this led to quantum computing.
I also posted about our Antifragility paper, where the non-positiveness of the transfer function between Gamma and Vega can also be interpreted as some negative implied volatility, something physically realizable, which, as we discussed, can be related to Simpson paradox for the far out-of-the-money behavior of stochastic processes.
I wish that the contenders of subtle notions who claim "common sense" would better know what they are talking about and show the necessary rigor in their alleged mathematical criticism!
Academics are so easily busted on X.
Next we deal with that idiot, the econometrician @sndurlauf who isn't aware of its uses in finance, so separated from the real world & unaware of it that it is not even funny.
BTW Espen (my coauthor) & I shared trading office space back in the days in Connecticut. tweet
Alex Bilzerian
RT @alexbilz: 'There is nothing in a stochastic differential equation that is not in a Fokker-Planck equation, but the stochastic differential equation is so much easier to write down and manipulate that only an excessively zealous purist would try to eschew the technique.' - C.W. Gardiner
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RT @alexbilz: 'There is nothing in a stochastic differential equation that is not in a Fokker-Planck equation, but the stochastic differential equation is so much easier to write down and manipulate that only an excessively zealous purist would try to eschew the technique.' - C.W. Gardiner
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Alex Bilzerian
'p-Adic Probability Theory and its Generalizations' - Andrei Khrennikov (2006, PDF):
https://t.co/rpVUR8LN7e
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'p-Adic Probability Theory and its Generalizations' - Andrei Khrennikov (2006, PDF):
https://t.co/rpVUR8LN7e
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Alex Bilzerian
RT @alexbilz: 'The Mathematics of Gambling: Getting Rich' - Ed Thorp in The Gambling Times (1980, PDF):
https://t.co/qx7pV1IGF1
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RT @alexbilz: 'The Mathematics of Gambling: Getting Rich' - Ed Thorp in The Gambling Times (1980, PDF):
https://t.co/qx7pV1IGF1
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Alex Bilzerian
RT @ma_sabba: @alexbilz Yep there is a lot of incompetence in academia. Factors contributing to this include increasing scarcity of talented people (if a suitable hire isn't possible, they'll fill the vacancy with literally anybody), poor/nonexistent leadership, and lack of accountability.
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RT @ma_sabba: @alexbilz Yep there is a lot of incompetence in academia. Factors contributing to this include increasing scarcity of talented people (if a suitable hire isn't possible, they'll fill the vacancy with literally anybody), poor/nonexistent leadership, and lack of accountability.
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Alex Bilzerian
RT @alexbilz: Excellent problem: https://t.co/Lp5vWDcT3g
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RT @alexbilz: Excellent problem: https://t.co/Lp5vWDcT3g
'Probability Through Problems' - Marek Capinski & Tomasz Zastawniak (PDF):
https://t.co/DblB4NfBW6 tweet
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Alex Bilzerian
RT @alexbilz: 'Feynman's approach to negative probability in quantum mechanics' - Scully, Walther & Schleich (1994, PDF):
https://t.co/uXB4BK9gl5
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RT @alexbilz: 'Feynman's approach to negative probability in quantum mechanics' - Scully, Walther & Schleich (1994, PDF):
https://t.co/uXB4BK9gl5
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