Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a unique corresponding output value. Stochastic simulators, however, have intrinsic randomness due to their use of (pseudo)random numbers, so they give different results when run twice with the same input parameters but non-common random numbers. Due to this random nature, conventional Sobol' indices, used in global sensitivity analysis, can be extended to stochastic simulators in different ways. In this paper, we discuss three possible extensions and focus on those that depend only on the statistical dependence between input and output. This choice ignores the detailed data generating process involving the internal randomness, and can thus be applied to a wider class of problems. We propose to use the generalized lambda model to emulate the response distribution of stochastic simulators. Such a surrogate can be constructed without the need for replications. The proposed method is applied to three examples including two case studies in finance and epidemiology. The results confirm the convergence of the approach for estimating the sensitivity indices even with the presence of strong heteroskedasticity and small signal-to-noise ratio

Spillover effects among financial institutions: a state-dependent sensitivity value-at-risk approach : [Version September 2012]

In this paper, we develop a state-dependent sensitivity value-at-risk (SDSVaR) approach that enables us to quantify the direction, size, and duration of risk spillovers among financial institutions as a function of the state of financial markets (tranquil, normal, and volatile). Within a system of quantile regressions for four sets of major financial institutions (commercial banks, investment banks, hedge funds, and insurance companies) we show that while small during normal times, equivalent shocks lead to considerable spillover effects in volatile market periods. Commercial banks and, especially, hedge funds appear to play a major role in the transmission of shocks to other financial institutions. Using daily data, we can trace out the spillover effects over time in a set of impulse response functions and find that they reach their peak after 10 to 15 days

How close are time series to power tail L\'evy diffusions?

This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as $\alpha$-stable L\'evy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition this approach gives evidence for heavy tails in data sets of precipitable water vapor of the Western Tropical Pacific.Comment: 30 pages, 10 figure

The individual contribution to income inequality: conceptual analysis and empirical investigation

The paper aims to study individual contributions to income inequality. The role of individual positions in the analysis of inequality is considered at various levels. The utility of inequality analysis in analysing the variation across a given income distribution is also recognised. The paper elaborates on this perspective and proposes a definition of individual contributions to inequality within a given income distribution. The concept of such an individual contribution is proposed, and its properties are discussed. The paper presents and tests the hypothesis that given the concept of individual contributions, patterns of influence associated with the determinants of inequality can be identified across a given income distribution. An empirical method of investigation and testing is proposed based on the Survey on Household Income and Wealth carried out by the Bank of Italy. The results support the hypothesis and show that the patterns identified are useful in the analysis of inequality.Inequality; person-by-person perspective; quantile regression