Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit

We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. More precisely, we prove that the empirical measure (respectively the discretised density) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in $L^1_{loc}$) to the unique Kruzkov entropy solution of the conservation law. The initial data are taken in $L^1\cap L^\infty$, nonnegative, and with compact support, hence we are able to handle densities with vacuum. Our result holds for a reasonably general class of velocity maps (including all the relevant examples in the applications, e.g. in the Lighthill-Whitham-Richards model for traffic flow) with possible degenerate slope near the vacuum state. The proof of the result is based on discrete BV estimates and on a discrete version of the one-sided Oleinik-type condition. In particular, we prove that the regularizing effect $L^1\cap L^\infty \mapsto BV$ for nonlinear scalar conservation laws is intrinsic of the discrete model

On the complete model with stochastic volatility by Hobson and Rogers

We examine a recent model, proposed by Hobson and Rogers, which generalizes the classical one by Black and Scholes for pricing derivative securities such as options and futures. We treat the numerical solution of some degenerate partial differential equations governing this financial problem and propose some new numerical schemes which naturally apply in this degenerate setting. Then we aim to emphasize the mathematical tractability of the Hobson-Rogers model by presenting analytical and numerical results comparable with the known ones in the classical Black-Scholes environment.Black-Scholes model, stochastic volatility, path-dependent option, hypoelliptic equation

Condensation phenomena in nonlinear drift equations

We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we prove existence and uniqueness for measure solutions. Moreover, we prove that all solutions blow up in finite time leading to a concentration of mass only at the origin, and the concentrated mass absorbs increasingly the mass converging to the total mass as time goes to infinity. Our analysis makes a substantial use of independent variable scalings and pseudo-inverse functions techniques

Policy Uncertainty, Symbiosis, and the Optimal Fiscal and Monetary Conservativeness

This paper extends a well-known macroeconomic stabilization game between monetary and fiscal authorities introduced by Dixit and Lambertini (American Economic Review, 93: 1522-1542) to multiplicative (policy) uncertainty. We find that even if fiscal and monetary authorities share a common output and inflation target (i.e. the symbiosis assumption), the achievement of the common targets is no longer guaranteed; under multiplicative uncertainty, in fact, a time consistency problem arises unless policymakers� output target is equal to the natural level.Monetary-fiscal policy interactions, uncertainty, symbiosis.

Policy Uncertainty, Symbiosis, and the Optimal Fiscal and Monetary Conservativeness

This paper extends the stabilization game between monetary and fiscal authorities to the case of multiplicative (model) uncertainty. In this context, the “symbiosis assumption”, i.e. fiscal and monetary policy share the same ideal targets, no longer guarantees the achievement of ideal output and inflation, unless the ideal output is equal to its natural level. A time consistency problem arises.Monetary-fiscal policy interactions, uncertainty, symbiosis.

A stochastic estimated version of the Italian dynamic General Equilibrium Model (IGEM)

We estimate with Bayesian techniques the Italian dynamic General Equilibrium Model (IGEM), which has been developed at the Italian Treasury Department, Ministry of Economy and Finance, to assess the effects of alter-native policy interventions. We analyze and discuss the estimated effects of various shocks on the Italian economy. Compared to the calibrated version used for policy analysis, we find a lower wage rigidity and higher adjustment costs. The degree of prices and wages indexation to past inflation is much smaller than the indexation level assumed in the calibrated model. No substantial difference is found in the estimated monetary parameters. Estimated fiscal multipliers are slightly smaller than those obtained from the calibrated version of the model