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...

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to both sample and population size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially...

We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or...

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of...

Using Jeff Holman's comments in Quantitative Finance to illustrate 4 critical errors students should learn to avoid: 1) Mistaking tails (4th moment) for volatility (2nd moment), 2) Missing Jensen's Inequality, 3) Analyzing the hedging wihout the underlying, 4) The necessity of a numeraire in...

Religions come with risk-​managing interdicts and heuristics, and they carry such interdicts and heuristics across generations. We remark on such facets of religion in relation to a propensity among some decision scientists and others to regard practices that they cannot understand as being...

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...