Risk Minimization and Optimal Derivative Design in a Principal Agent Game

We consider the problem of Adverse Selection and optimal derivative design within a Principal-Agent framework. The principal's income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She evaluates her risk using a coherent and law invariant risk measure and tries minimize her exposure by selling derivative securities on her income to individual agents. The agents have mean-variance preferences with heterogeneous risk aversion coefficients. An agent's degree of risk aversion is private information and hidden to the principal who only knows the overall distribution. We show that the principal's risk minimization problem has a solution and illustrate the effects of risk transfer on her income by means of two specific examples. Our model extends earlier work of Barrieu and El Karoui (2005) and Carlier, Ekeland and Touzi (2007).Comment: 28 pages, 4 figure

Synchronization of networks with variable local properties

We study the synchronization transition of Kuramoto oscillators in scale-free networks that are characterized by tunable local properties. Specifically, we perform a detailed finite size scaling analysis and inspect how the critical properties of the dynamics change when the clustering coefficient and the average shortest path length are varied. The results show that the onset of synchronization does depend on these properties, though the dependence is smooth. On the contrary, the appearance of complete synchronization is radically affected by the structure of the networks. Our study highlights the need of exploring the whole phase diagram and not only the stability of the fully synchronized state, where most studies have been done up to now.Comment: 5 pages and 3 figures. APS style. Paper to be published in IJBC (special issue on Complex Networks' Structure and Dynamics

Transition Temperature of a Magnetic Semiconductor with Angular Momentum j

We employ dynamical mean-field theory to identify the materials properties that optimize Tc for a generalized double-exchange (DE) model. We reach the surprising conclusion that Tc achieves a maximum when the band angular momentum j equals 3/2 and when the masses in the 1/2 and 3/2 sub-bands are equal. However, we also find that Tc is significantly reduced as the ratio of the masses decreases from one. Consequently, the search for dilute magnetic semiconductors (DMS) materials with high Tc should proceed on two fronts. In semiconductors with p bands, such as the currently studied Mn-doped Ge and GaAs semiconductors, Tc may be optimized by tuning the band masses through strain engineering or artificial nanostructures. On the other hand, semiconductors with s or d bands with nearly equal effective masses might prove to have higher Tc's than p-band materials with disparate effective masses.Comment: 5 pages, 4 figure

Discrete-time Markov chain approach to contact-based disease spreading in complex networks

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at a certain rate from an infected vertex to one neighbor at a time, and the reactive process (RP) in which an infected individual effectively contacts all its neighbors to expand the epidemics. However, a more realistic scenario is obtained from the interpolation between these two cases, considering a certain number of stochastic contacts per unit time. Here we propose a discrete-time formulation of the problem of contact-based epidemic spreading. We resolve a family of models, parameterized by the number of stochastic contact trials per unit time, that range from the CP to the RP. In contrast to the common heterogeneous mean-field approach, we focus on the probability of infection of individual nodes. Using this formulation, we can construct the whole phase diagram of the different infection models and determine their critical properties.Comment: 6 pages, 4 figures. Europhys Lett (in press 2010

Information theory of quantum systems with some hydrogenic applications

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.Comment: 9 pages, 3 figure