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Nassim Nicholas Taleb

Publications and source records attributed to Nassim Nicholas Taleb.

25 records · Page 2Linked to original sources
arXiv2016

On the shadow moments of apparently infinite-mean phenomena

We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a heavy- tailed distribution with an extremely wide yet bounded support. We introduce the concept of dual distribution, by means of a log-transformation that removes the upper bound. The tail of the dual distribution can then be studied using extreme value theory, without making excessive parametric assumptions, and the estimates one obtains can be used to study the original distribution and compute its moments by reverting the log- transformation. The central difference between our approach and a simple truncation is in the smoothness of the transformation between the original and the dual distribution, allowing use of extreme value theory. War casualties, operational risk, environment blight, complex networks and many other econophysics phenomena are possible fields of application.

stat.AP↗
arXiv2015

On the statistical properties and tail risk of violent conflicts

We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data. We introduce a novel approach to apply extreme value theory to fat-tailed variables that have a remote, but nonetheless finite upper bound, by defining a corresponding unbounded dual distribution (given that potential war casualties are bounded by the world population). We apply methods from extreme value theory on the dual distribution and derive its tail properties. The dual method allows us to calculate the real mean of war casualties, which proves to be considerably larger than the sample mean, meaning severe underestimation of the tail risks of conflicts from naive observation. We analyze the robustness of our results to errors in historical reports, taking into account the unreliability of accounts by historians and absence of critical data. We study inter-arrival times between tail events and find that no particular trend can be asserted. All the statistical pictures obtained are at variance with the prevailing claims about "long peace", namely that violence has been declining over time.

stat.AP↗
arXiv2015

How to (Not) Estimate Gini Coefficients for Fat Tailed Variables

Direct measurements of Gini coefficients by conventional arithmetic calculations are a poor estimator, even if paradoxically, they include the entire population, as because of super-additivity they cannot lend themselves to comparisons between units of different size, and intertemporal analyses are vitiated by the population changes. The Gini of aggregated units A and B will be higher than those of A and B computed separately. This effect becomes more acute with fatness of tails. When the sample size is smaller than entire population, the error is extremely high. The conventional literature on Gini coefficients cannot be trusted and comparing countries of different sizes makes no sense; nor does it make sense to make claims of "changes in inequality" based on conventional measures. We compare the standard methodologies to the indirect methods via maximum likelihood estimation of tail exponent. We compare to the tail method which is unbiased, with considerably lower error rate. We also consider measurement errors of the tail exponent and suggest a simple but efficient methodology to calculate Gini coefficients.

q-fin.ST↗
arXiv2014

Tail Risk Constraints and Maximum Entropy

In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution of the underlying asset returns is fully known. In practice, both the performance criteria and the informational structure are markedly different: risk-taking agents are mandated to build portfolios by primarily constraining the tails of the portfolio return to satisfy VaR, stress testing, or expected shortfall (CVaR) conditions, and are largely ignorant about the remaining properties of the probability distributions. As an alternative, we derive the shape of portfolio distributions which have maximum entropy subject to real-world left-tail constraints and other expectations. Two consequences are (i) the left-tail constraints are sufficiently powerful to overide other considerations in the conventional theory, rendering individual portfolio components of limited relevance; and (ii) the "barbell" payoff (maximal certainty/low risk on one side, maximum uncertainty on the other) emerges naturally from this construction.

q-fin.RM↗
arXiv2014

The Precautionary Principle (with Application to the Genetic Modification of Organisms)

We present a non-naive version of the Precautionary (PP) that allows us to avoid paranoia and paralysis by confining precaution to specific domains and problems. PP is intended to deal with uncertainty and risk in cases where the absence of evidence and the incompleteness of scientific knowledge carries profound implications and in the presence of risks of "black swans", unforeseen and unforeseable events of extreme consequence. We formalize PP, placing it within the statistical and probabilistic structure of ruin problems, in which a system is at risk of total failure, and in place of risk we use a formal fragility based approach. We make a central distinction between 1) thin and fat tails, 2) Local and systemic risks and place PP in the joint Fat Tails and systemic cases. We discuss the implications for GMOs (compared to Nuclear energy) and show that GMOs represent a public risk of global harm (while harm from nuclear energy is comparatively limited and better characterized). PP should be used to prescribe severe limits on GMOs.

q-fin.GN↗
arXiv2013

Where Do Thin Tails Come From?

The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the probability distribution of the response to a random variable. We introduce a general dose-response curve and argue that the left and right-boundedness or saturation of the response in natural things leads to thin-tails, even when the "underlying" random variable at the source of the exposure is fat-tailed.

q-fin.RM↗