They almost had."The function [$]f(x) = a e^{-bx^2}[$] is believed to have first appeared for approximating large binomial coefficients in the 2nd edition (1718) of Doctrine of Chances by Abraham de Moivre (a book on probability)."

QuoteOriginally posted by: katastrofaThey almost had."The function [$]f(x) = a e^{-bx^2}[$] is believed to have first appeared for approximating large binomial coefficients in the 2nd edition (1718) of Doctrine of Chances by Abraham de Moivre (a book on probability)."1718 was not in the XVII but in the XVIII century. You know, 0-based numbering, like in C++...

The deeper problem with Gauss isn't the choice of distribution so much as it is the belief in an independent distribution of some kind to be found by clever analytics or clever data mining. The edifice of all these models is built on a foundational notion of exogenous shocks -- that something outside the system perturbs the system -- and that we will model those perturbations. Exogenous shocks may have been a valid model in an agrarian age when price yields were a function of crop yields and crop yields were a function of the caprice of the weather. But the current economy is much more divorced from nature and much more internally coupled (some might even argue that the weather is now a function of the economy and not the other way around!). That endogenous coupling is especially strong at the financial level and in derivatives (e.g., see 1987, flash crashes, etc.).Given a growing stream of recent historical economic data (asset returns, company fundamentals, default rates, macro data, etc.) that contain no fat tail events, what is the likely change in the optimal leverage and risk management protocols? And how does that change in leverage and risk management (e.i. increase in leverage, loosen the controls) affect price appreciation? And with steady price appreciation, we see a continued data stream with no fat tails which validates our hypothesis about returns. But these feedback loops can be unstable, especially where the time-scale of decision making (e.g., buy/sell, invest here/invest there?) is much shorter than the time-scale of knowledge creation (e.g., will this asset actually generate the expected future cashflows?). Technically, this is a feed-forward control system and it won't be stable. Moreover, when a fat tail does happen, investors and regulators change their behaviour, so the structure of the system changes which both justifies people ignoring that the latest historical fat-tail (i.e., "now that we know about it, we can protect against it") and sets up the same pattern of stable data leading to systemically unstable risk management practices to create the next fat tail.

QuoteOriginally posted by: UltravioletQuoteOriginally posted by: katastrofaThey almost had."The function [$]f(x) = a e^{-bx^2}[$] is believed to have first appeared for approximating large binomial coefficients in the 2nd edition (1718) of Doctrine of Chances by Abraham de Moivre (a book on probability)."1718 was not in the XVII but in the XVIII century. You know, 0-based numbering, like in C++...Yes, that's why I said they almost had it! De Moivre was late by 19 years. QuoteOriginally posted by: Traden4AlphaGiven a growing stream of recent historical economic data (asset returns, company fundamentals, default rates, macro data, etc.) that contain no fat tail events, what is the likely change in the optimal leverage and risk management protocols? And how does that change in leverage and risk management (e.i. increase in leverage, loosen the controls) affect price appreciation? And with steady price appreciation, we see a continued data stream with no fat tails which validates our hypothesis about returns. But these feedback loops can be unstable, especially where the time-scale of decision making (e.g., buy/sell, invest here/invest there?) is much shorter than the time-scale of knowledge creation (e.g., will this asset actually generate the expected future cashflows?). Technically, this is a feed-forward control system and it won't be stable. Moreover, when a fat tail does happen, investors and regulators change their behaviour, so the structure of the system changes which both justifies people ignoring that the latest historical fat-tail (i.e., "now that we know about it, we can protect against it") and sets up the same pattern of stable data leading to systemically unstable risk management practices to create the next fat tail.The thesis that capitalism is unstable is not exactly new. Just very inconvenient for almost everyone except the people who reject the system.

QuoteOriginally posted by: katastrofaQuoteOriginally posted by: UltravioletQuoteOriginally posted by: katastrofaThey almost had."The function [$]f(x) = a e^{-bx^2}[$] is believed to have first appeared for approximating large binomial coefficients in the 2nd edition (1718) of Doctrine of Chances by Abraham de Moivre (a book on probability)."1718 was not in the XVII but in the XVIII century. You know, 0-based numbering, like in C++...Yes, that's why I said they almost had it! De Moivre was late by 19 years. QuoteOriginally posted by: Traden4AlphaGiven a growing stream of recent historical economic data (asset returns, company fundamentals, default rates, macro data, etc.) that contain no fat tail events, what is the likely change in the optimal leverage and risk management protocols? And how does that change in leverage and risk management (e.i. increase in leverage, loosen the controls) affect price appreciation? And with steady price appreciation, we see a continued data stream with no fat tails which validates our hypothesis about returns. But these feedback loops can be unstable, especially where the time-scale of decision making (e.g., buy/sell, invest here/invest there?) is much shorter than the time-scale of knowledge creation (e.g., will this asset actually generate the expected future cashflows?). Technically, this is a feed-forward control system and it won't be stable. Moreover, when a fat tail does happen, investors and regulators change their behaviour, so the structure of the system changes which both justifies people ignoring that the latest historical fat-tail (i.e., "now that we know about it, we can protect against it") and sets up the same pattern of stable data leading to systemically unstable risk management practices to create the next fat tail.The thesis that capitalism is unstable is not exactly new. Just very inconvenient for almost everyone except the people who reject the system.What would make a computer (run by a simple operating system) really stable? Allocate memory fix and monopolize processors by a few failure-tolerant operations .. "Capitalism" seeks stability by fixed allocations of "capital storage" and monopolized economic transactions ....? But because it was unacceptable if 100% ... , some residual memory and processors are available for free economic programming - with dynamic memory management ... a complex system still run by a quite simple operation system? Damned to learn from its turbulences (things love uncertainty - now we are with NNT again?).

Talebs's 7 rules of Antifragility in Research1. Convexity is easier to attain than knowledge ("long-gamma" property)2. A 1/N is almost always the best with convex strategies (dispersion property)3. Serial optionality (cliquet property)4. Nonnarrative research (optionality property)5. Theory is born from practice (nonteleological property)6. Premium for simplicity (less-is-more property)7. Better cataloguing of negative results (via negative property)from Understanding is a poor substitute for convexityp.s. from a business stand point I agree with optionality and cliquet properties - it is impossible now to work along rigid business plans and models, even strategies can become dangerous (if you don't see a disruption ..). But, IMO, theory and practice run in co-evolution (at least in math).

Can we have this expressed in less pompous terms?

6. Premium for simplicity (less-is-more property)<=>?

QuoteOriginally posted by: Ultraviolet0-based numbering, like in C++...Maybe you mean like in C? In C++ you can overload operator[] and make it start from 1.

QuoteOriginally posted by: katastrofaCan we have this expressed in less pompous terms?exactly+1

QuoteOriginally posted by: DevonFangsMaybe you mean like in C? In C++ you can overload operator[] and make it start from 1.Evil. Very evil.

QuoteOriginally posted by: DevonFangsQuoteOriginally posted by: Ultraviolet0-based numbering, like in C++...Maybe you mean like in C? In C++ you can overload operator[] and make it start from 1.No, I meant C++. I don't have bad programming habits.

QuoteOriginally posted by: katastrofaCan we have this expressed in less pompous terms?I haven't read Taleb's recent works. But I read fooled by randomness, and this is what I got from that book:1. Shit happens (shit property)2. So, don't invest in shit you don't understand (anti-shit property)3. It is inevitable that shit will hit the fan, at which point everything will be covered in shit. (the fan property)4. Important to recognize that some (shitty) people make money from fan sales, but won't be there for the clean up. (shitty people property)...

Reads like a self-help book for investors. Most recommended.

Taleb loses what little sense of humour he has on twitter