Theory of fuzzy integrals and its applications

Foundations Of Statistics

Stochastic equations in infinite dimensions

Inflammatory cytokines in depression: Neurobiological mechanisms and therapeutic implications

https://www.cell.com/trends/neurosciences/pdf/S0166-2236(00)01661-1.pdf

Interleukin 1 in the brain: biology, pathology and therapeutic target

The RT-PCR analysis of RNA from progenitor and differentiated primary rat oligodendrocytes, and from the oligodendrocyte CG-4 cell line, shows the presence of the IL-1beta mRNA, the type I IL-1beta receptor and the IL-1 receptor accessory protein in these cells. In situ hybridization of a rat IL-1beta probe to primary progenitor and differentiated rat oligodendrocytes results in a positive signal. The double hybridization of the IL-1beta probe, together with an oligodendrocyte-specific differentiation marker, to sections of postnatal rat brain at different stages of differentiation is also positive. The double immuno-labelling technique utilized indicates coincidence of the signals on the brain slices. The results show that IL-1beta mRNA is constitutively expressed in rat brain oligodendrocytes from 1 day after birth onward. In agreement with this observation, CG-4 cells, primary progenitor and differentiated rat oligodendrocytes are positively stained by antibodies against IL-1beta. Postnatal brain slices from 1 and 4 day old and adult rats, labelled with a double immunofluorescence technique, are also stained by antibodies against IL-1beta. This signal coincides with that of antibodies against oligodendrocyte-specific surface markers. We conclude that IL-1beta is constitutively expressed in rat brain progenitor and differentiated oligodendrocytes.

Constitutive Expression of Interleukin-1beta (IL-1beta) in Rat Oligodendrocytes

https://economics.yale.edu/sites/default/files/files/Workshops-Seminars/Econometrics/cherubini-110330b.pdf

A copula-based model of speculative price dynamics in discrete time

. In this paper we analyse a stochastic volatility model that is an extension of the traditional Black-Scholes one. We price European options on several assets by using a superstrategy approach. We characterize the Markov superstrategies, and show that they are linked to a nonlinear PDE, called the Black-Scholes-Barenblatt (BSB) equation. This equation is the Hamilton-Jacobi-Bellman equation of an optimal control problem, which has a nice financial interpretation. Then we analyse the optimization problem included in the BSB equation and give some sufficient conditions for reduction of the BSB equation to a linear Black-Scholes equation. Some examples are given.

Robustness of the Black-Scholes approach in the case of options on several assets

We propose an innovative theoretical model to determine the optimal hedge ratio (OHR) with futures contracts as the minimizer of a quantile risk measure. This class of measures is very large and allows to recover the minimum-VaR and the minimum-expected shortfall hedge ratios as special cases. The copula representation of quantiles yields an accurate and flexible estimation of the dependence structure between the spot and the futures position. Employing data for the main UK and US indices, and EUR/USD and EUR/GBP exchange rates, we investigate the hedging effectiveness of our model compared to that of existing approaches. We document that our model improves upon the hedging performance of minimum-VaR and minimum-expected shortfall hedge ratios, provided that the copula shows an acceptable fit to the data. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:658–675, 2014

A Copula‐Based Quantile Risk Measure Approach to Estimate the Optimal Hedge Ratio

We propose a general treatment of random variables aggregation accounting for the dependence among variables and bounded or unbounded support of their sum. The approach is based on the extension to the concept of convolution to dependent variables, involving copula functions. We show that some classes of copula functions (such as Marshall–Olkin and elliptical) cannot be used to represent the dependence structure of two variables whose sum is bounded, while Archimedean copulas can be applied only if the generator becomes linear beyond some point. As for the application, we study the problem of capital allocation between risks when the sum of losses is bounded.

Silvia Romagnoli

Papers

Constitutive Expression of Interleukin-1beta (IL-1beta) in Rat Oligodendrocytes

A copula-based model of speculative price dynamics in discrete time

Robustness of the Black-Scholes approach in the case of options on several assets

A Copula‐Based Quantile Risk Measure Approach to Estimate the Optimal Hedge Ratio

On the distribution of the (un)bounded sum of random variables