Pasquale Cirillo

Are your data really Pareto distributed

Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers and models justifying the presence of power laws in economic data.

On the statistical properties and tail risk of violent conflicts

We examine statistical pictures of violent conflicts over the last 2000 years, providing techniques for dealing with the unreliability of historical data.

Duality and stationary distributions of wealth distribution models

We analyze a class of energy and wealth redistribution models, characterizing their stationary measures and showing that they have a discrete dual process. In particular we show that the wealth distribution model with non-zero saving propensity can never have invariant product measures. We also introduce diffusion processes associated to the wealth distribution models by ‘instantaneous thermalization’.

The Boulogne fish market: the social structure and the role of loyalty

We examine the Boulogne wholesale fish market, analysing the structure of the trading network between sellers and buyers. Differently from other works in the literature, our analysis indicates a significant amount of ‘bilateral loyalty’ seller–buyer. Loyalty is from buyers to a few sellers as well as from sellers to a few buyers. We also show that loyalty has an impact on prices, discriminating among agents.

A NONPARAMETRIC URN-BASED APPROACH TO INTERACTING FAILING SYSTEMS WITH AN APPLICATION TO CREDIT RISK MODELING

In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter- acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes.

Expected Shortfall Estimation for Apparently Infinite-Mean Models of Operational Risk

Statistical analyses on actual data depict operational risk as an extremely heavy-tailed phenomenon, able to generate losses so extreme as to suggest the use of infinite-mean models. But no loss can actually destroy more than the entire value of a bank or of a company, and this upper bound should be considered when dealing with tail-risk assessment. Introducing what we call the dual distribution, we show how to deal with heavy-tailed phenomena with a remote yet finite upper bound. We provide methods to compute relevant tail quantities such as the Expected Shortfall, which is not available under infinite-mean models, allowing adequate provisioning and capital allocation. This also permits a measurement of fragility. The main difference between our approach and a simple truncation is in the smoothness of the transformation between the original and the dual distribution. Our methodology is useful with apparently infinite-mean phenomena, as in the case of operational risk, but it can be applied in all those situations involving extreme fat tails and bounded support.

Gini estimation under infinite variance

We study the problems related to the estimation of the Gini index in presence of a fat-tailed data generating process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index

An Analysis of the Number of Medical Malpractice Claims and Their Amounts

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An urn model for cascading failures on a lattice

). We show that, in such a case, the Gini coefficient cannot be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges under fat tails. This has important implications for the ongoing discussion about economic inequality. We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution, as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We also show how the nonparametric Gini bias increases with lower values of

Introducing Bottom-up Adaptive Macroeconomics

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