A non-local inequality and global existence

In this article we prove a collection of new non-linear and non-local integral inequalities. As an example for $u\ge 0$ and $p\in (0,\infty)$ we obtain \int_{\threed} dx ~ u^{p+1}(x) \le (\frac{p+1}{p})^2 \int_{\threed} dx ~ \{(-\triangle)^{-1} u(x) \} \nsm \nabla u^{\frac{p}{2}}(x)\nsm^2. We use these inequalities to deduce global existence of solutions to a non-local heat equation with a quadratic non-linearity for large radial monotonic positive initial conditions. Specifically, we improve \cite{ksLM} to include all $\alpha\in (0, 74/75)$.Comment: 6 pages, to appear in Advances in Mathematic

La Pedemontana lombarda: ottant'anni di progetti.

open2La Pedemontana lombarda: un percorso lungo e tortuoso accompagna il progetto che da più di quarant’anni fa riferimento allo stesso tracciatoS.Rinelli; P.VillaniRinelli, Savino; Villani, PAOLA MARIA CHIAR

An R&D Investment Game under Uncertainty in Real Option Analysis

One of the problems of using the financial options methodolgy to analyse investment decisions is that strategic considerations become extremely important. So, the theory of real option games combines two successful theories, namely real options and game theory. The value of flexibility can be valued as a real option while the competition can be analyzed with game theory. In our model we develop an interaction between two firms that invest in R&D. The firm that invests first, defined as the Leader, acquires a first mover advantage that we assume as a higher share of market. But the R&D investments present positive externalities and so, the option exercise by the Leader generates an Information Revelation that benefits the Follower.Real Options; Exchange Options; Option games; Information Revelation.

Valutazione di opzioni exchange attraverso la simulazione Monte Carlo e stima delle sensitivita'.

Exchange options give the holder the right to exchange the asset V for the asset D. They present an important role for the evaluation of investment projects which have uncertainty both in the gross value (underlying asset) and in the investment costs (exercise price). In this paper we propose to elaborate some MATLAB algorithms to estimate exchange options with Monte Carlo simulation. Then, through the estimate and analysis of sensitivity, we compare the most important exchange options emphasizing the american sequential exchange option.Exchange Options; Real Options; Monte Carlo Simulation;

A Monte Carlo comparison of Bayesian testing for cointegration rank

This article considers a Bayesian testing for cointegration rank, using an approach developed by Strachan and van Dijk (2007), that is based on Koop, Leon-Gonzalez, and Strachan (2006). The Bayes factors are calculated for selecting cointegrating rank. We calculate the Bayes factors using two methods - the Schwarz BIC approximation and Chib's (1995) algorithm for calculating the marginal likelihood. We run Monte Carlo simulations to compare the two methods.