Generalized rationing problems and solutions

An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims on some amount of a scarce resource, but also by some exogenous ex-ante conditions (initial stock of resource or net worth of agents, for instance), different from claims. Within this framework, we define a generalization of the constrained equal awards rule. We provide two different characterizations of this generalized rule. Finally, we use the corresponding dual properties to characterize a generalization of the constrained equal losses rule

Decentralized rationing problems [WP]

Decentralized rationing problems are those in which the resource is not directly assigned to agents, but first allocated to groups of agents and then divided among their members. Within this framework, we define extensions of the constrained equal awards, the constrained equal losses and the proportional rules. We show that the first two rules do not preserve certain essential properties and prove the conditions under which both rules do preserve those properties. We characterize the extension of the proportional rule as the only solution that satisfies individual equal treatment of equals. We prove that the proportional rule is the only solution that assigns the same allocation regardless of whether the resource is distributed directly to agents or in a decentralized manner (with agents grouped). Finally, we analyse a strategic game based on decentralized rationing problems in which agents can move freely across groups to submit their claims

Introducing migratory flows in life table construction

The purpose of life tables is to describe the mortality behav iour of particular groups. The construction of general life tables is based on death statis tics and census figures of resident populations under the hypothesis of closed demographic sys tem. Among other assumptions, this hypothesis implicitly assumes that entries (immigrants) a nd exits (emigrants) of the population are usually not significant (being almost of the same magnitu de for each age compensating each other). This paper theoretically extends the classical sol ution to open demographic systems and studies the impact of this hypothesis in constructing a life table. In particular, using the data of residential variations made available to the public by the S panish National Statistical Office (INE, Instituto Nacional de Estad ́ ıstica) to approximate migratory flows, we introduce in the p rocess of constructing a life table these flows and compare, before and after graduation, the crude mortality rates and the adjusted death probabilities obtained when mi gratory flows are, and are not, taken into accountPeer Reviewe

Rationing problems with payoff thresholds

An extension of the standard rationing model is introduced. Agents are not only identi fied by their respective claims over some amount of a scarce resource, but also by some payoff thresholds. These thresholds introduce exogenous differences among agents (full or partial priority, past allocations, past debts, ...) that may influence the final distribution. Within this framework we provide generalizations of the constrained equal awards rule and the constrained equal losses rule. We show that these generalized rules are dual from each other. We characterize the generalization of the equal awards rule by using the properties of consistency, path-independence and compensated exemption. Finally, we use the duality between rules to characterize the generalization of the equal losses solution

Análisis y evaluación de hipótesis implícitas en la construcción de tablas de mortalidad

En el campo actuarial y demográfico la incidencia de la mortalidad, reflejada en la tabla de mortalidad, es utilizada en varias disciplinas. Por ejemplo, en el sistema público de pensiones o en los seguros de vida del sector asegurador. Para poblaciones generales, históricamente estas tablas han sido construidas utilizando una serie de hipótesis implícitas relativas a los distintos eventos demográficos: defunciones, migraciones y nacimientos. Sin embargo, en los últimos años hemos asistido a una explosión de información disponible, unido a una revolución en los sistemas informáticos, que mediante el desarrollo de los estimadores adecuados permite mejorar las estimaciones que actualmente se realizan en el estudio de la mortalidad. En la construcción de la tabla de mortalidad se utilizan distintas hipótesis de manera implícita que dependen de la familia y tipo de estimadores que se empleen, y cuya necesidad depende de los niveles de información disponibles. Cuando se trabaja con estimadores de periodo AP (period based-estimator), basados en mx, algunas de las hipótesis implícitas habituales consisten en asumir: (i) distribución uniforme de fallecimientos para cada edad y año, (ii) sistema demográfico cerrado o sistema demográfico abierto con hipótesis implícita de distribución uniforme de migraciones y (iii) distribución uniforme de las fechas de cumpleaños de todos los individuos de la población que no mueren a lo largo del año. Es interesante señalar que, si el estimador que se emplea está basado en el comportamiento de la cohorte durante un periodo bianual AC (bianual-period cohort-based), basadas en qx, de las tres hipótesis comentadas anteriormente, la última es innecesaria. Teniendo presente qué información está disponible en relación a la mortalidad, así como las tres hipótesis formuladas previamente, el objetivo de esta tesis es múltiple. En primer lugar, se construyen, para cada familia de estimadores, AP o AC, nuevos estimadores, cada uno de los cuales considera ninguna, alguna o varias de las hipótesis anteriores (i), (ii) y (iii). Esto, que en sí mismo ya representa una aportación en el campo de la metodología estadística, se complementa poniendo de manifiesto cómo ciertos estimadores utilizados habitualmente, en ocasiones por inercia del pasado, pueden no ser los más adecuados cuando la información a la que se tiene acceso es más detallada y se requiere cierta precisión en los resultados. Por otro lado, para medir el impacto que los estimadores propuestos pueden tener en poblaciones reales se evalúan las hipótesis que implícitamente se asumen mediante test estadísticos de diferente naturaleza: contrastes de hipótesis espaciales, funcionales y paramétricos. En relación a la información utilizada, en todos los casos se emplean datos oficiales, los cuales han sido proporcionados por el Instituto Nacional de Estadística (INE), en lo que corresponde a la población española, y por el Instituto Valenciano de Estadística (IVE), al abordar un estudio más detallado sobre la población de la Comunitat Valenciana. El software utilizado ha sido R y Matlab.In the actuarial and demographic field, the incidence of mortality, reflected in the life table, is used in different disciplines. For instance, in the public pensions system or in life insurance in the insurance sector. Historically, for general populations these tables have been built using a series of implicit hypotheses concerning different demographic events: deaths, migrations and births. However, in recent years we have witnessed an explosion of available information that, together with a revolution in information technology systems, through the development of appropriate estimators, enables improvements in the estimations that are currently made in the study of mortality. Different hypotheses are used implicitly in the construction of the life table, depending on the family and type of estimators used; and the need for them depends on the available levels of information. When working with period estimators AP (period based-estimator), based on mx, some of the usual implicit hypotheses consist of assuming: (i) uniform distribution of deaths for each age and year; (ii) closed population system or open population system with implicit hypothesis of uniform distribution of migrations; and (iii) uniform distribution of the births of all individuals who do not die throughout the year. It is interesting to note that, if the estimator used is based on the behaviour of the cohort during a biannual period AC (biannual-period cohort-based), based on qx, of the three hypotheses discussed above, the latter is unnecessary. Bearing in mind what information is available in relation to mortality, as well as the three hypotheses previously formulated, the aim of this thesis is multiple. On the one hand, new estimators are constructed for each family of estimators, AP or AC, each of which considers none, one, or several of the previous hypotheses (i), (ii) and (iii). This, which already represents a contribution to the field of statistical methodology, is complemented by showing how certain estimators customarily used, sometimes by inertia of the past, may not be the most adequate when the accessible information is more detailed and certain precision is required in the results. On the other hand, to measure the impact that the proposed estimators can have on real populations, the implicitly assumed hypotheses are evaluated using statistical tests of different natures: contrasts of spatial, functional and parametric hypotheses. In relation to the information used, official data is utilised in all cases, provided by the Spanish Official Statistical Agency (INE), in what corresponds to the Spanish population, and the Valencian Institute of Statistics (IVE), when approaching a more detailed study of the population of the Comunitat Valenciana. The software used were R and Matlab

Rationing problems with ex-ante conditions

An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims to some amount of a scarce resource, but also by some exogenous ex-ante conditions (initial stock of resource or net worth of agents, for instance), other than claims. Within this framework,we define a generalization of the constrained equal awards rule and provide two different characterizations of this generalized rule. Finally, we use the corresponding dual properties to characterize a generalization of the constrained equal losses rule

Introducing migratory flows in life table construction

The purpose of life tables is to describe the mortality behaviour of particular groups. The construction of general life tables is based on death statistics and census figures of resident populations under the hypothesis of closed demographic system. Among other assumptions, this hypothesis implicitly assumes that entries (immigrants) and exits (emigrants) of the population are usually not significant (being almost of the same magnitude for each age compensating each other). This paper theoretically extends the classical solution to open demographic systems and studies the impact of this hypothesis in constructing a life table. In particular, using the data of residential variations made available to the public by the Spanish National Statistical Office (INE, Instituto Nacional de Estadística) to approximate migratory flows, we introduce in the process of constructing a life table these flows and compare, before and after graduation, the crude mortality rates and the adjusted death probabilities obtained when migratory flows are, and are not, taken into account

Elaboració d’un reglament de règim intern per a l’escola d’un centre penitenciari: La presó d’Albocàsser

Quinzenes Jornades de Foment de la Investigació de la FCHS (Any 2009-2010

Estimation of the combined effects of ageing and seasonality on mortality risk: An application to Spain

Despite the overwhelming evidence that shows the persistence of intra-annual variations on demographic events (deaths, birth dates and migration flows), life tables are computed and provided on an annual basis. This paper develops a new estimator for estimating sub-annual death rates that, considering the exact moment of occurrence (exact age and day) of events, concurrently accounts for ageing and calendar fluctuations. This paper also shows how modelling the intra-annual variations of death rates, through specific seasonal–ageing indexes, can be used as a tool for constructing new sub-annual tables from annual tables. This new methodology is exemplified using a real database of Spain made up of 186 million demographic events (1.5 million of which are deaths), from which seasonal–ageing indexes are estimated and conclusions drawn. First, seasonal effects are, as a rule, stronger than ageing effects. For a given integer age, season has a higher impact on increasing or decreasing the average risk of death at that age than the actual age of the exposed-to-risk. Second, the intensity of the effects varies among seasons and age-quarters. Third, neither seasonal nor ageing effects are age-stationary. Their impact, be it to varying degrees, intensifies as people get older. Fourth, there is interaction between seasonal and ageing effects. In short, life expectancies and probabilities of dying/surviving not only depend on people's age, but also on when their birthday falls within the year. This has implications, for instance, in managing pension systems or for insurance companies

Constrained multi-issue rationing problems

We study a variant of the multi-issue rationing model, where agents claim for several issues. In this variant, the available amount of resource intended for each issue is constrained to an amount fixed a priori according to exogenous criteria. The aim is to distribute the amount corresponding to each issue taking into account the allocation for the rest of issues (issue-allocation interdependence). We name these problems constrained multi-issue allocation situations (CMIA). In order to tackle the solution to these problems, we first reinterpret some single-issue egalitarian rationing rules as a minimization program based on the idea of finding the feasible allocation as close as possible to a specific reference point. We extend this family of egalitarian rules to the CMIA framework. In particular, we extend the constrained equal awards rule, the constrained equal losses rule and the reverse Talmud rule to the multi-issue rationing setting, which turn out to be particular cases of a family of rules, namely the extended α-egalitarian family. This family is analysed and characterized by using consistency principles (over agents and over issues) and a property based on the Lorenz dominance criterion