Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Embedding theorems of function classes, IV

Vegeu el resum a l'inici del document del fitxer adjunt

Embedding theorems of function classes, II

Vegeu el resum a l'inici del document del fitxer adjunt.

The period function of the generalized Lotka-Volterra centers

"Vegeu el resum a l'inici del document del fitxer adjunt"

Embedding theorems of function classes, I

"Vegeu el resum a l'inici del document del fitxer adjunt."

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

L'Efecte dels raigs gamma sobre les pastanagues: recerca i innovació a la cuina del segle XXI

Conferència inagural de la 11a Setmana de la Ciència celebrada el 2006 al Palau Robert

A new look at the Heston characteristic function

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factorization of the moment generating function as product of Bessel type factors, and an approximating sequence to the law of log-spot is deduced.

Aspects of Iwasawa theory over function fields

"Vegeu el resum a l'inici del document del fitxer adjunt."

Cirp function and characterisation in RNA and microRNAs

In order to search for novel genes involved in cell proliferation, the hypothesis was that by infecting primary cells with a cDNA library of immortal cells would render immortalizing genes. Consequently it has been discovered CIRP (Cold inducible RNA-binding protein). Mammalian cells exposed to mild hypothermia show a general inhibition of protein synthesis and a concomitant increase in the expression of a small number of cold-shock mRNAs and proteins. Rbm3, another RNA binding protein belonging to the same family, has been postulated to facilitate protein synthesis at mild cold shock. To investigate if the same occurs for CIRP, CIRP was overexpressed in primary cells and protein sintesis was measured. Interestingly, CIRP increased protein synthesis, however, such increase did not involve an increase in the polysome fraction or affected the ribosome profile. In addition, the effect caused by CIRP inhibition or knockdown was also analyzed. Different siRNAs against CIRP were tested. Once checked their efficiency by decreasing CIRP at mRNA and protein levels, proliferation was tested by BrdU, cell number (DAPI) and proliferation curves were performed. Interestingly, CIRP provoke a decreased proliferation in primary cells: MEFs, HMEC; and cancer cells: TERA2 and HeLa. In conclusion, we describe for the first time that CIRP bypasses replicative senescence when over-expressed at physiological temperature (37ºC) by increasing a general protein synthesis. This effect is achieved through ERK1/2 activation in MEFs.The decrease in growth rate found in mammalian cells treated with mild cold stress is not entirely attributable to arrested metabolism. This decrease may also involve an active process in which CIRP and other stress-responsive proteins play a fundamental role in stimulating proliferation. Although most cell proteins are down-regulated or inhibited with cold stress, CIRP is activated to maintain cells in an active proliferative status and its overexpression at 37°C might be potentially oncogenic.

Emissió ràdio a baixa freqüència en fenòmens eruptius i en fonts esteses de raigs gamma d'alta i molt alta energia

La tasca investigadora presentada en aquesta memòria s'ha centrat en les fonts galàctiques de raigs gamma de molt alta energia LS I +61 303, HESS J1708-410 i HESS J1858+020. La primera és una binària de raigs gamma molt estudiada, formada per una estrella massiva i un objecte compacte. S'ha proposat un escenari on l'objecte compacte seria un púlsar jove, i la interacció del seu vent amb el vent de l'estrella generaria els raigs gamma. De totes formes, no s'ha detectat polsos procedents d'aquest putatiu púlsar. L'investigador va realitzar observacions en fase a 1280 MHz amb el radiotelescopi GMRT, sense trobar-hi polsos, cosa que implica un estricte límit superior de 0,38 mJy a la densitat mitjana de flux polsat en un putatiu púlsar amb un període major que 2 mil•lisegons en el sistema binari LS I +61 303. Per altra banda, HESS J1708-410 i HESS J1858+020 són dues fonts esteses de raigs gamma de molt alta energia de les quals no es coneix cap contrapart a d'altres longituds d'ona. L'investigador les va observar amb el GMRT, quatre vegades HESS J1708-410 (dues a 610 MHz i dues a 1400 MHz) i dues vegades HESS J1858+020 (una a cada freqüència). En les imatges realitzades amb aquestes dades no hi ha emissió estesa coincident amb les regions d'emissió de raigs gamma. HESS J1858+020 se solapa parcialment amb una font estesa que podria ser un SNR. De confirmar-se la falta de contrapartida ràdio de HESS J1708-410, estaríem parlant d'un accelerador hadrònic extraordinàriament eficient, d'una classe desconeguda fins ara.

Variability of North Atlantic hurricanes: seasonal versus individual-event features

Tropical cyclones are affected by a large number of climatic factors, which translates into complex patterns of occurrence. The variability of annual metrics of tropical-cyclone activity has been intensively studied, in particular since the sudden activation of the North Atlantic in the mid 1990’s. We provide first a swift overview on previous work by diverse authors about these annual metrics for the North-Atlantic basin, where the natural variability of the phenomenon, the existence of trends, the drawbacks of the records, and the influence of global warming have been the subject of interesting debates. Next, we present an alternative approach that does not focus on seasonal features but on the characteristics of single events [Corral et al., Nature Phys. 6, 693 (2010)]. It is argued that the individual-storm power dissipation index (PDI) constitutes a natural way to describe each event, and further, that the PDI statistics yields a robust law for the occurrence of tropical cyclones in terms of a power law. In this context, methods of fitting these distributions are discussed. As an important extension to this work we introduce a distribution function that models the whole range of the PDI density (excluding incompleteness effects at the smallest values), the gamma distribution, consisting in a powerlaw with an exponential decay at the tail. The characteristic scale of this decay, represented by the cutoff parameter, provides very valuable information on the finiteness size of the basin, via the largest values of the PDIs that the basin can sustain. We use the gamma fit to evaluate the influence of sea surface temperature (SST) on the occurrence of extreme PDI values, for which we find an increase around 50 % in the values of these basin-wide events for a 0.49 C SST average difference. Similar findings are observed for the effects of the positive phase of the Atlantic multidecadal oscillation and the number of hurricanes in a season on the PDI distribution. In the case of the El Niño Southern oscillation (ENSO), positive and negative values of the multivariate ENSO index do not have a significant effect on the PDI distribution; however, when only extreme values of the index are used, it is found that the presence of El Niño decreases the PDI of the most extreme hurricanes.