On the viscosity solutions of a stochastic differential utility problem

We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for degenerate nonlinear partial differential equation. We also characterize the solution in the vanishing viscosity sense.Viscosity solution, Burgers' equation, Stochastic differential utility

CVA and vulnerable options pricing by correlation expansions

We consider the problem of computing the Credit Value Adjustment ({CVA}) of a European option in presence of the Wrong Way Risk ({WWR}) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in \cite{AS}. We compare the numerical performance of such a method with that recently proposed by Brigo et al. (\cite{BR18}, \cite{BRH18}) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.Comment: 21 page

Stability of backward stochastic differential equations

AbstractThis paper studies the stability of the solution of backward stochastic differential equations. The stability of the solution is here intended as robustness under small perturbations of the coefficients and of the boundary values. The work is suggested by the interest the results might have in finance theory

The role of public, non governmental and private actors for the development of organic farming: the Italian successful example.

The authors analyse the growth of organic agro-food sector in Italy and explain the relationships between private operators, NGOs and various levels of governance (municipalities, regions, central government), which have been acting (in various forms) for the development of organic agriculture and food processing / distribution

Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriate discretization scheme of the solution of the Mc Kean-Vlasov equation introduced by Bossy and Talay. More specifically, we consider approximations of the distribution and of the density of the solution of the stochastic differential equation associated to the Mc Kean - Vlasov equation. The scheme adopted here is a mixed one: Euler/weakly interacting particle system. If $n$ is the number of weakly interacting particles and $h$ is the uniform step in the time discretization, we prove that the rate of convergence of the distribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of the order of $\frac 1{\sqrt n} + h$, while for the densities is of the order $h +\frac 1 {\sqrt {nh}}$. This result is obtained by carefully employing techniques of Malliavin Calculus.Mc Kean-Vlasov equation, Malliavin calculus

Origin of Roman worked stones from St. Saturno christian Basilica (south Sardinia, Italy)

The work aims to define the origin of the architectural stone elements worked by Romans and reused in the St. Saturno Basilica, between the late Antiquity and Romanesque periods. Thus, different rocks (marbles, various facies of limestones, volcanic rocks) used to construct the ancient building were sampled and analysed. All the different kinds of stones were sampled from the Basilica, taking precise reference to the various construction phases and structural changes of the monument occurred in the centuries. The sedimentary and volcanic lithologies belong to the local outcrops of Cagliari Miocenic geological formation (e.g. limestone) and to other volcanic outcrops of south Sardinia, respectively. By means of a multi-method archaeometric study (mineralogical-petrographic observations on thin sections and O-18 vs C-13 stable isotope ratio analysis), the provenance of classical marbles used for manufacturing Roman architectural elements (column shafts, bases, capitals, slabs, etc.) were defined, which are thought to come from extra-regional sources. The results show that the marbles come mainly from Apuan Alps (Italy) and subordinately from Greek quarrying areas

A moment matching method for option pricing under stochastic interest rates

In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black & Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching technique applied to a conditional Black & Scholes formula, is quite general and it applies to various models, whether affine or not. To check its accuracy and computational time, we implement it for the CIR interest rate model correlated with the underlying, using the Monte Carlo simulations as a benchmark. The method's performance turns out to be quite remarkable, even when compared with analogous results obtained by the affine approximation technique presented in Grzelak and Oosterlee (2011) and by the expansion formula introduced in Kim and Kunimoto (1999), as we show in the last section

A Bayesian estimate of the superfluid moments of inertia from the 2016 glitch in the Vela pulsar

The observation of the first pulse-to-pulse glitch in the Vela pulsar opens a new window on theoretical speculations about the internal dynamics of neutron stars, as it allows to test models for the description of the first moments in a glitch. We improve the analytical study of the minimal three-component model for pulsar glitches, by solving it with generic initial conditions for the two initial lags of the superfluid components. The purpose is to use this solution to fit the data of the 2016 Vela glitch - by employing a Bayesian approach - and to obtain a probability distribution for the physical parameters of the model and for observational parameters like the glitch rise time and the relaxation timescale. A physically reasonable, non-informative prior has been set on the different parameters of the model, so that the posterior distribution can be compared with state-of-the-art information obtained from microphysical calculations. By considering a model with a tightened prior on the moment of inertia fractions and by comparing it with the original model by means of Bayesian model selection, we study the possibility of a crust-limited superfluid reservoir. The posterior distribution for the moment of inertia fractions of the superfluid components, the coupling parameters and the initial velocity lags between the components has been obtained. Analysis of the inferred posterior also confirms the presence of an overshoot in that glitch, and sets an upper limit of 6 seconds on the glitch rise timescale. The comparison between the two models with different priors on the moment of inertia fractions seems to indicate the necessity of a core participation in the glitch phenomenon, regardless of the uncertain strength of the entrainment coupling.Comment: 12 pages, 5 figures. Comments welcom

Making big data work: smart, sustainable, and safe cities

The goal of the present thematic series is to showcase some of the most relevant contributions submitted to the ‘Telecom Italia Big Data Challenge 2014’ and to provide a discussion venue about recent advances in the appplication of mobile phone and social media data to the study of individual and collective behaviors. Particular attention is devoted to data-driven studies aimed at understanding city dynamics. These studies include: modeling individual and collective traffic patterns and automatically identifying areas with traffic congestion, creating high-resolution population estimates for Milan inhabitants, clustering urban dynamics of migrants and visitors traveling to a city for business or tourism, and investigating the relationship between urban communication and urban happiness