Lorenz-based quantitative risk management

In this thesis, we address problems of quantitative risk management using a specific set of tools that go under the name of Lorenz curve and inequality indices, developed to describe the socio-economic variability of a random variable.Quantitative risk management deals with the estimation of the uncertainty that isembedded in the activities of banks and other financial players due, for example, tomarket fluctuations. Since the well-being of such financial players is fundamental for the correct functioning of the economic system, an accurate description and estimation of such uncertainty is crucial.Applied ProbabilityNumerical Analysi

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 α∈(1,2)). 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 α. We then prove that maximum likelihood estimation outperforms nonparametric methods, requiring a much smaller sample size to reach efficiency. Finally, for fat-tailed data, we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution

High flow nasal therapy in perioperative medicine: from operating room to general ward

Abstract Background High flow nasal therapy (HFNT) is a technique in which humidified and heated gas is delivered to the airways through the nose via small nasal prongs at flows that are higher than the rates generally applied during conventional oxygen therapy. The delivered high flow rates combine mixtures of air and oxygen and enable different inspired oxygen fractions ranging from 0.21 to 1. HFNT is increasingly used in critically ill adult patients, especially hypoxemic patients in different clinical settings. Main body Noninvasive ventilation delivers positive pressure (end-expiratory and inspiratory pressures or continuous positive airway pressure) via different external interfaces. In contrast, HFNT produces different physiological effects that are only partially linked to the generation of expiratory positive airway pressure. HFNT and noninvasive ventilation (NIV) are interesting non-invasive supports in perioperative medicine. HFNT exhibits some advantages compared to NIV because HFNT is easier to apply and requires a lower nursing workload. Tolerance of HFNT remains a matter of intense debate, and it may be related to selected parameters. Patients receiving HFNT and their respiratory patterns should be closely monitored to avoid delays in intubation despite correct oxygenation parameters. Conclusion HFNT seems to be an interesting noninvasive support in perioperative medicine. The present review provides anesthesiologists with an overview of current evidence and practical advice on the application of HFNT in perioperative medicine in adult patients