ABSTRACT
Riskiness is a key issue in a broad number of situations, spanning from finance to insurance and economics. Because of this ubiquitous role, the specialized literature deeply examined risk; the works of (Arrow, 1951) and (Pratt, 1953), for instance, introduced the risk-aversion coefficient ρu, to monitor the general attitude of investors towards risk, once given their utility function u. Alternatives to ρu have been widely explored too, with riskiness primarily associated with the dispersion of the random variable employed to represent outcomes (Markowitz, 1952, Markowitz, 1959, Tobin, 1958). As a consequence, the riskiness of alternative investments can also be evaluated by means of the standard deviation or, more generally, by means of any function that belongs to the family of the so called deviation measures (Rockafellar et al., 2006). The flourishing of risk-related studies reached the peak in latest years of the past century, when JP Morgan in 1996 released a new measure: the Value at Risk (VaR). VaR has proved to have superior qualities than variance/standard deviation, and as such is more suitable to characterize risky investments. Since its introduction, VaR has rapidly became the standard in finance industry, although searching for alternatives like coherent risk measures (Artzner et al, 1999) or objective measure of risk (Aumann and Serrano, 2008; Foster and Hart, 2012; Marina and Resta, 2013), to cite some examples, has practically never stopped. Indeed, alternatives have often superior mathematical features than VaR, by they have not (or not yet) conquered a great consensus among practitioners, because they are harder to be practically implemented.
