Herramientas estadísticas para el estudio de perfiles de riesgo

En este documento se ilustra de un modo práctico, el empleo de tres instrumentos que permiten al actuario definir grupos arancelarios y estimar premios de riesgo en el proceso que tasa la clase para el seguro de no vida. El primero es el análisis de segmentación (CHAID y XAID) usado en primer lugar en 1997 por UNESPA en su cartera común de coches. El segundo es un proceso de selección gradual con el modelo de regresión a base de distancia. Y el tercero es un proceso con el modelo conocido y generalizado de regresión linear, que representa la técnica más moderna en la bibliografía actuarial. De estos últimos, si combinamos funciones de eslabón diferentes y distribuciones de error, podemos obtener el aditivo clásico y modelos multiplicativos

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Sequential decisions in allocation problems

[eng] In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequentia decision problem. In each step of process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentally compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersections of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantagenous properties for the first player

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Vertical Syndication-Proof Competitive Prices in Multilateral Markets

[eng] A multi-sided Böhm-Bawerk assignment game (Tejada, to appear) is a model for a multilateral market with a finite number of perfectly complementary indivisible commodities owned by different sellers, and inflexible demand and support functions. We show that for each such market game there is a unique vector of competitive prices for the commodities that is vertical syndication-proof, in the sense that, at those prices, syndication of sellers each owning a different commodity is neither beneficial nor detrimental for the buyers. Since, moreover, the benefits obtained by the agents at those prices correspond to the nucleolus of the market game, we provide a syndication-based foundation for the nucleolus as an appropriate solution concept for market games. For different solution concepts a syndicate can be disadvantageous and there is no escape to Aumman’s paradox (Aumann, 1973). We further show that vertical syndicationproofness and horizontal syndication-proofness – in which sellers of the same commodity collude – are incompatible requirements under some mild assumptions. Our results build on a self-interesting link between multi-sided Böhm-Bawerk assignment games and bankruptcy games (O’Neill, 1982). We identify a particular subset of Böhm-Bawerk assignment games and we show that it is isomorphic to the whole class of bankruptcy games. This isomorphism enables us to show the uniqueness of the vector of vertical syndication-proof prices for the whole class of Böhm-Bawerk assignment market using well-known results of bankruptcy problems.

Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

On the coincidence between the Shimomura's bargaining sets and the core

[cat] En l'article es dona una condició necessària per a que els conjunts de negociació definits per Shimomura (1997) i el nucli d'un joc cooperatiu amb utilitat transferible coincideixin. A tal efecte, s'introdueix el concepte de vectors de màxim pagament. La condició necessària consiteix a verificar que aquests vectors pertanyen al nucli del joc.

TrkB signaling is required for postnatal survival of CNS neurons and protects hippocampal and motor neurons from axotomy-induced cell death

Newborn mice carrying targeted mutations in genes encoding neurotrophins or their signaling Trk receptors display severe neuronal deficits in the peripheral nervous system but not in the CNS. In this study, we show that trkB (¿/¿) mice have a significant increase in apoptotic cell death in different regions of the brain during early postnatal life. The most affected region in the brain is the dentate gyrus of the hippocampus, although elevated levels of pyknotic nuclei were also detected in cortical layers II and III and V and VI, the striatum, and the thalamus. Furthermore, axotomized hippocampal and motor neurons of trkB (¿/¿) mice have significantly lower survival rates than those of wild-type littermates. These results suggest that neurotrophin signaling through TrkB receptors plays a role in the survival of CNS neurons during postnatal development. Moreover, they indicate that TrkB receptor signaling protects subpopulations of CNS neurons from injury- and axotomy-induced cell death.

Regional and cellular patterns of reelin mRNA expression in the forebrain of the developing and adult mouse

The reelin gene encodes an extracellular protein that is crucial for neuronal migration in laminated brain regions. To gain insights into the functions of Reelin, we performed high-resolution in situ hybridization analyses to determine the pattern of reelin expression in the developing forebrain of the mouse. We also performed double-labeling studies with several markers, including calcium-binding proteins, GAD65/67, and neuropeptides, to characterize the neuronal subsets that express reelin transcripts. reelinexpression was detected at embryonic day 10 and later in the forebrain, with a distribution that is consistent with the prosomeric model of forebrain regionalization. In the diencephalon, expression was restricted to transverse and longitudinal domains that delineated boundaries between neuromeres. During embryogenesis,reelin was detected in the cerebral cortex in Cajal-Retzius cells but not in the GABAergic neurons of layer I. At prenatal stages, reelin was also expressed in the olfactory bulb, and striatum and in restricted nuclei in the ventral telencephalon, hypothalamus, thalamus, and pretectum. At postnatal stages, reelin transcripts gradually disappeared from Cajal-Retzius cells, at the same time as they appeared in subsets of GABAergic neurons distributed throughout neocortical and hippocampal layers. In other telencephalic and diencephalic regions,reelin expression decreased steadily during the postnatal period. In the adult, there was prominent expression in the olfactory bulb and cerebral cortex, where it was restricted to subsets of GABAergic interneurons that co-expressed calbindin, calretinin, neuropeptide Y, and somatostatin. This complex pattern of cellular and regional expression is consistent with Reelin having multiple roles in brain development and adult brain function.

TrkB and TrkC signaling are required for maturation and synaptogenesis of hippocampal connections

Recent studies have suggested a role for neurotrophins in the growth and refinement of neural connections, in dendritic growth, and in activity-dependent adult plasticity. To unravel the role of endogenous neurotrophins in the development of neural connections in the CNS, we studied the ontogeny of hippocampal afferents intrkB (¿/¿) and trkC (¿/¿) mice. Injections of lipophilic tracers in the entorhinal cortex and hippocampus of newborn mutant mice showed that the ingrowth of entorhinal and commissural/associational afferents to the hippocampus was not affected by these mutations. Similarly, injections of biocytin in postnatal mutant mice (P10¿P16) did not reveal major differences in the topographic patterns of hippocampal connections. In contrast, quantification of biocytin-filled axons showed that commissural and entorhinal afferents have a reduced number of axon collaterals (21¿49%) and decreased densities of axonal varicosities (8¿17%) in both trkB (¿/¿) and trkC (¿/¿) mice. In addition, electron microscopic analyses showed thattrkB (¿/¿) and trkC (¿/¿) mice have lower densities of synaptic contacts and important structural alterations of presynaptic boutons, such as decreased density of synaptic vesicles. Finally, immunocytochemical studies revealed a reduced expression of the synaptic-associated proteins responsible for synaptic vesicle exocytosis and neurotransmitter release (v-SNAREs and t-SNAREs), especially in trkB (¿/¿) mice. We conclude that neither trkB nor trkC genes are essential for the ingrowth or layer-specific targeting of hippocampal connections, although the lack of these receptors results in reduced axonal arborization and synaptic density, which indicates a role for TrkB and TrkC receptors in the developmental regulation of synaptic inputs in the CNS in vivo. The data also suggest that the genes encoding for synaptic proteins may be targets of TrkB and TrkC signaling pathways.

Measures of ionicity of alkaline-earth oxides from the analysis of ab initio cluster wave functions

We present an analysis of the M-O chemical bonding in the binary oxides MgO, CaO, SrO, BaO, and Al2O3 based on ab initio wave functions. The model used to represent the local environment of a metal cation in the bulk oxide is an MO6 cluster which also includes the effect of the lattice Madelung potential. The analysis of the wave functions for these clusters leads to the conclusion that all the alkaline-earth oxides must be regarded as highly ionic oxides; however, the ionic character of the oxides decreases as one goes from MgO, almost perfectly ionic, to BaO. In Al2O3 the ionic character is further reduced; however, even in this case, the departure from the ideal, fully ionic, model of Al3+ is not exceptionally large. These conclusions are based on three measures, a decomposition of the Mq+-Oq- interaction energy, the number of electrons associated to the oxygen ions as obtained from a projection operator technique, and the analysis of the cation core-level binding energies. The increasing covalent character along the series MgO, CaO, SrO, and BaO is discussed in view of the existing theoretical models and experimental data.

Ionic-covalent transition in titanium oxides

The nature of the chemical bond in three titanium oxides of different crystal structure and different formal oxidation state has been studied by means of the ab initio cluster-model approach. The covalent and ionic contributions to the bond have been measured from different theoretical techniques. All the analysis is consistent with an increasing of covalence in the TiO, Ti2O3, and TiO2 series as expected from chemical intuition. Moreover, the use of the ab initio cluster-model approach combined with different theoretical techniques has permitted us to quantify the degree of ionic character, showing that while TiO can approximately be described as an ionic compound, TiO2 is better viewed as a rather covalent oxide.

Industrial agglomerations and wage gradients: the Spanish economy in the interwar period

This paper gives new evidence on the relationship between integration and industrial agglomeration in the presence of scale economies, by testing directly one of the predictions that can be derived from Krugman (1991), that is, the existence of regional nominal wage gradients and its transformation following changes in trade regimes. Our case study analyzes the effects of the substitution of an open economy by a closed economy regime, exactly the opposite process studied by Hanson (1996, 1997). In Spain, during the interwar period, protectionist policies would have favored the loss of centrality of the coastal location (Barcelona) and the relative rise of central locations (such as Madrid). Our results indicate the existence of a wage gradient centered in Barcelona during the interwar period (1914-1930) and its weakening after 1925.