A lending scheme for a system of interconnected banks with probabilistic constraints of failure

We derive a closed form solution for an optimal control problem related to an interbank lending schemes subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to a real banks network by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network

Generalized adjoint forms on algebraic varieties

We prove a full generalization of the Castelnuovo's free pencil trick. We show its analogies with the Adjoint Theorem; see L. Rizzi, F. Zucconi, Differential forms and quadrics of the canonical image, arXiv:1409.1826 and also Theorem 1.5.1 in G. P. Pirola, F. Zucconi, Variations of the Albanese morphisms, J. Algebraic Geom. 12 (2003), no. 3, 535-572. Moreover we find a new formulation of the Griffiths's infinitesimal Torelli Theorem for smooth projective hypersurfaces using meromorphic $1$-forms.Comment: 18 page

Differential forms and quadrics of the canonical image

Let $\pi\colon\mathcal{X}\to B$ be a family over a smooth connected analytic variety $B$, not necessarily compact, whose general fiber $X$ is smooth of dimension $n$, with irregularity $\geq n+1$ and such that the image of the canonical map of $X$ is not contained in any quadric of rank $\leq 2n+3$. We prove that if the Albanese map of $X$ is of degree $1$ onto its image then the fibers of $\pi\colon\mathcal{X}\to B$ are birational under the assumption that all the $1$-forms and all the $n$-forms of a fiber are holomorphically liftable to $\mathcal{X}$. Moreover we show that generic Torelli holds for such a family $\pi\colon \mathcal{X}\to B$ if, in addition to the above hypothesis, we assume that the fibers are minimal and their minimal model is unique. There are counterexamples to the above statements if the canonical image is contained inside quadrics of rank $\leq 2n+3$. We also solve the infinitesimal Torelli problem for an $n$-dimensional variety $X$ of general type with irregularity $\geq n+1$ and such that its cotangent sheaf is generated and the canonical map is a rational map whose image is not contained in a quadric of rank less or equal to $2n+3$.Comment: 23 pages, revised version incorporating referees' comments, exposition improve

A note on Torelli-type theorems for Gorenstein curves

Using the notion of generalized divisors introduced by Hartshorne, we adapt the theory of adjoint forms to the case of Gorenstein curves. We show an infinitesimal Torelli-type theorem for vector bundles on Gorenstein curves. We also construct explicit counterexamples to the infinitesimal Torelli claim in the case of a reduced reducible Gorenstein curve.Comment: 17 page

Geometric realizations and duality for Dahmen-Micchelli modules and De Concini-Procesi-Vergne modules

We give an algebraic description of several modules and algebras related to the vector partition function, and we prove that they can be realized as the equivariant K-theory of some manifolds that have a nice combinatorial description. We also propose a more natural and general notion of duality between these modules, which corresponds to a Poincar\'e duality-type correspondence for equivariant K-theory.Comment: Final version, to appear on Discrete and Computational Geometr

The monetary transmission mechanism; evidence from the industries of five OECD countries

This paper presents new evidence on the monetary transmission mechanism based on the effects of unexpected monetary policy shocks on 21 manufacturing industries in 5 OECD countries (France, Germany, Italy, the UK and the US). The goal is twofold. First, to document the crossindustry heterogeneity of monetary policy effects. Second, to explain this heterogeneity in terms of microeconomic characteristics suggested by theory, using an original firmlevel database. The results highlight the following empirical regularities; (i) a significant crossindustry heterogeneity of policy effects; (ii) a similar crossindustry distribution of policy effects across countries. These patterns are systematically related to industry output durability and investmentintensity and to measures of firms' borrowing capacity, size and interest payment burden. Quantitatively, the "credit channel" variables are as significant as the traditional variables (durability, investment intensity) in explaining the differential impact of monetary policy.monetary policy transmission, balance sheet data

A note on optimal commodity taxation with moral hazard and separable preferences

In this paper we show that differential commodity taxation is superfluous in an economy with moral hazard and separable preferences.Moral Hazard, Separable Preferences, Optimal Commodity Taxation