An Analytical Approach to Merton’s Rational Option Pricing Theory

In the early 70s Merton developed a theory based on economic arguments to study the properties of option and warrant prices. The main tool in his proofs was the portfolio dominance principle. In the context where the price of a contingent claim satisfies a partial differential equation we provide analytical proofs of Merton’s rational option pricing theory. We use several versions of the maximum principle as well as the sliding and the moving planes methods to prove our results. Our approach enables us to extend the theory to nonlinear models.Merton, rational theory, option pricing, Black-Scholes, maximum principle

A Selection Criterion for Patterns in Reaction-Diffusion Systems

Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided certain conditions are met. Turing's proposal has already been confirmed as a pattern formation mechanism in several chemical and biological systems and, due to their wide applicability, there is a great deal of interest in deciphering how to generate specific patterns under controlled conditions. However, techniques allowing one to predict what kind of spatial structure will emerge from Turing systems, as well as generalized reaction-diffusion systems, remain unknown. Here, we consider a generalized reaction diffusion system on a planar domain and provide an analytic criterion to determine whether spots or stripes will be formed. It is motivated by the existence of an associated energy function that allows bringing in the intuition provided by phase transitions phenomena. This criterion is proved rigorously in some situations, generalizing well known results for the scalar equation where the pattern selection process can be understood in terms of a potential. In more complex settings it is investigated numerically. Our criterion can be applied to efficiently design Biotechnology and Developmental Biology experiments, or simplify the analysis of hypothesized morphogenetic models.Comment: 19 pages, 10 figure

Continuous Choreographies as Limiting Solutions of NN-body Type Problems with Weak Interaction

We consider the limit $N\to +\infty$ of $N$-body type problems with weak interaction, equal masses and $-\sigma$-homogeneous potential, $0<\sigma<1$. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equation is the Euler-Lagrange equation of a corresponding limiting action functional. Our main result is that the circle is the absolute minimizer of the action functional among zero mean (travelling wave) loops of class $H^1$

The Effect of the Shape of the Domain on the Existence of Solutions of an Equation Involving the Critical Sobolev Exponent

AbstractWe study the critical Sobolev exponent equation. By imposing some conditions on the shape of the domain we are able to obtain existence and multiplicity of positive solutions. In particular, multiplicity results for contractible domains are presented, based on an approach that allows us to generalize previous work by Ding, who had proved an existence result for a contractible domain

Parasitized mates increase infection risk for partners

Peer reviewedPublisher PD

Passive Microstrip Transmitarray Lens for Ku Band

The aim of this paper is to introduce a novel 12 GHz radiating design based on the idea of transmitarray lens device. In this document, an overview of the functioning of this kind of devices is given and the proposed transmitarray lens is studied, with architecture discussion and selection, as well as some ideas about the design, and manufacturing. In the document, some design, manufacturing and validation of the constituting elements of the lens (radiating elements, transmission circuits and transitions) are presented, together with a complete prototype of assembled transmitarray lens. Radiation pattern measurements in anechoic chamber, as well as gain and directivity values are offered

Social context decouples the relationship between a sexual ornament and testosterone levels in a male wild bird

AbstractIn order to maximise fitness individuals should adjust their level of signalling according to their surrounding social environment. However, field experiments showing such adjustment of current signalling associated to changes in social context are lacking. Here, we manipulated levels of male aggressive- and dominance-related displays in a wild bird in our treated area by increasing testosterone levels using implants in a subset of males. We then compared the expression of sexual signals (i.e. comb size) between non-treated red grouse Lagopus lagopus scoticus males from control and treatment areas. We further explored the potential endocrinological mechanism linking social environment and signal expression by analysing testosterone levels in all males. Our treatment successfully increased overall aggressive- and dominance-related behaviours in the treatment area. Furthermore, testosterone-implanted birds increased their comb size as repeatedly shown in previous studies in male red grouse. Interestingly, untreated males living in the treatment area decreased their comb size, whilst increasing testosterone levels. Since comb size is a signal of dominance, untreated males from the treatment area may have perceived themselves as subordinate individuals and decreased their signalling levels to avoid confrontations with testosterone-treated, dominant individuals. In conclusion, our findings show that social context has the potential to regulate sexual signalling and testosterone levels. Our results highlight the role of social context when exploring the link between testosterone and behaviour, as it may reverse the relationship between both traits. Our results suggest that social context affects signalling and testosterone independently

Phase Shifter for Millimeter-Wave Frequency Range Based on Glide Symmetric Structures

The use of glide symmetry in radiofrequency devices to introduce dispersive effects has been recently proposed and demonstrated. One of these effects is to control the propagation constant of the structure. Here, we propose a mm-wave phase shifter whose elements have a glide-symmetric configuration to achieve a greater phase shift in the same waveguide space than the non-glide-symmetric case. The glide-symmetric phase shifter is implemented in waveguide technology and is formed by rows of metallic pins that produce the desired phase shift. To assess the better performance of the glide-symmetric phase shifter, it is compared to its non-glide-symmetric version whose metallic pins are located only in one of the broad sides of the waveguide. The operating frequency range of the phase shifter is 67 to 75 GHz. Results show a 180 degree phase shift in regard to the reference waveguide without pins, and 50 degrees more than the non-glide-symmetric version.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech