Statistik für bivariate gemischte Poisson–Prozesse am Beispiel der Kraftfahrthaftpflichtversicherung

Zusammenfassung: In diesem Artikel wird der Weg von einem univariaten gemischten Poisson–Prozess, der in vielen Bereichen zum Z?hlen von Ereignissen benutzt wird, zu einem bivariaten gemischten Poisson–Prozess aufgezeigt. Dazu werden einige Eigenschaften des bivariaten Prozesses angegeben. Im zweiten Teil der Arbeit wird gezeigt, wie mit Hilfe dieses Prozesses der übergang von einem herk?mmlichen Bonus–Malus–System in der Kraftfahrthaftpflichtversicherung zu einem Bonus–Malus–System mit Berücksichtigung der Schadenart beschritten werden kann. Dazu wird zuerst eine Modellprüfung der gegebenen Daten vorgenommen und sodann werden für verschiedene mischende Verteilungen die Verteilungsparameter gesch?tzt und Nettopr?mien angegeben sowie die Prognosegenauigkeit getestet.

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Summary: In this paper we show that the model of the bivariate mixed Poisson process arises in a natural way from the univariate mixed Poisson process, which is used in several areas for counting certain events. Furthermore we state some properties of the bivariate process. In the second part of the paper we illustrate how by means of the bivariate mixed Poisson process a bonus–malus system handling different types of accidents can be derived from the classical bonus–malus system in third–party liability insurance. To this end we first check the model on the given data and then estimate distribution parameters and compute net premiums for different mixing distributions as well as test the prediction probabilities.

* Vortrag am Dresdner Forum zur Versicherungsmathematik: Tarifierung in Erst- und Rückversicherung am 25. Juni 2004. Für die Unterstützung zu dieser Arbeit m?chte der Autor Lothar Partzsch, Klaus D. Schmidt (beide Dresden) und Friedemann Spies (München) recht herzlich danken.     

A Review of Kyoto Protocol Adoption in Russia: Joint Implementation in Focus

Russia’s role in ‘animation’ of the Kyoto Protocol was crucial. Its initial vacillation on ratification was predominantly due to political bargaining with the EU. Domestic economic rationales [i.e. impacts of emission trading and Joint Implementation (JI) projects] were important to a much lesser extent and environmental motives did not seem to play any role in the decision. Since the Protocol entered into force, there have been significant delays in complete establishment of policy implementation frameworks, which are necessary for Russia to start benefiting from JI and emission trading. Only recently, in 2007, have GHG inventories and a national registry been established and the responsibilities for implementation of the Protocol and JI among the government departments have been distributed only to a certain extent. Some constraints hindering JI projects, such as vague legislation, an unfavourable economic climate, lack of commitment to JI projects, corruption, xenophobia, state and agency ‘capture’ still remain.      

ATTITUDES TOWARDS THE EURO: AN EMPIRICAL STUDY BASED ON THE GERMAN SOCIO-ECONOMIC PANEL (SOEP)

This paper investigates changing attitudes towards the euro over time in Germany using longitudinal micro-data from the German Socio Economic Panel Study. We observe that a large part of the German population was worried about the new currency both before and after its introduction. Social psychological theories provide insight into these attitudes. Concerns regarding the euro are apparently connected with problems in handling the new currency and with the press coverage of price rises. For these reasons, future EMU member states should prepare their populations better for these challenges.     

Transformation using ( x + 0.5) to stabilize the variance of populations

Transformation is required to achieve homo-scedasticity when we perform ANOVA to test the effect of factors on population abundance. The effectiveness of transformations decreases when the data contain zeros. Especially, the logarithmic transformation or the Box–Cox transformation is not applicable in such a case. For the logarithmic transformation, 1 is traditionally added to avoid such problems. However, there is no concrete foundation as to why 1 is added rather than other constants, such as 0.5 or 2, although the result of ANOVA is much influenced by the added constant. In this paper, I suggest that 0.5 is preferable to 1 as an added constant, because a discrete distribution defined in {0, 1, 2, . . .} is approximately described by a corresponding continuous distribution defined in (0, ≧) if we add 0.5. Numerical investigation confirms this prediction. Received: October 16, 1998 / Accepted: June 10, 1999     

Strengths-Based Approach and Coping Strategies used by Parents Whose Young Children Exhibit Violent Behaviour: Collaboration Between Schools and Parents

This research study explores the strategies adopted by 60 parents of children between 3 and 9 years of age considered to have engaged in violent behaviour, within the meaning of the Safe Schools Act (Ontario Ministry of Education, Canada, 2000). This legal framework requires parents to be involved in the decisions concerning their children. Parents’ perceptions of their involvement lead them to develop coping strategies enabling them to play a more active role in such decision making. This article analyzes their perceptions according to a strengths-based approach and seeks to provide a mediation perspective to social work practice with families.

Imagined interactions,family money management patterns and coalitions,and attitudes toward money and credit

This study explores the imagined interactions college students have with their parents about money and credit, their attitudes toward credit and money, the ways they say their parents deal with financial decisions, and the communication coalitions regarding finances they perceive existing within their family. Students’ imagined interaction pleasantness is greatest when parents jointly form a plan for paying off credit card debt and lowest when parents argue. When family coalitions exist, students report more frequent imagined interactions. Imagined interaction frequency and pleasantness are related to credit and money attitudes.

Airline Negotiations and the New Concessionary Bargaining

I ask whether the highly confrontational collective bargaining in the airlines is unique to that industry or a sign of a deepening crisis in union–management relations nationally. First, airline labor relations are reviewed in the context of extremely contentious negotiations, intense industry competition, complex and fragmented bargaining structures, frequent bankruptcies, and unpredictable external shocks. Next, concessionary bargaining in the airlines is discussed, and a new and extreme form of concessionary bargaining is identified. The emergence of the new concessionary bargaining in the airlines and its spread to the automobile sector is then interpreted as the early signs of a fundamental transformation of collective bargaining. The implications of the new concessionary bargaining are then described at the workplace, company, union, and societal levels.

Disagreement over the immigration of low-income earners in a welfare state

This paper studies natives’ economically motivated preferences over different levels of immigration of low-income earners. Immigration affects natives through both intra- and intergenerational redistribution programmes and in the labour market. Our analysis suggests, in a welfare state that looks after the poor and the aged, economic motivation does not necessarily lead a native to have an extreme opinion on the preferable level of immigration, although it causes disagreement among natives. We find, regardless of parameter values, high-income earners prefer at least as much immigration as low-income earners who, in turn, prefer at least as much immigration as pensioners. The median voter is then likely to be a low-income native.

Integrated methodology for multiple systems estimation and record linkage using a missing data formulation

There are now three essentially separate literatures on the topics of multiple systems estimation, record linkage, and missing data. But in practice the three are intimately intertwined. For example, record linkage involving multiple data sources for human populations is often carried out with the expressed goal of developing a merged database for multiple system estimation (MSE). Similarly, one way to view both the record linkage and MSE problems is as ones involving the estimation of missing data. This presentation highlights the technical nature of these interrelationships and provides a preliminary effort at their integration.     

The additive hazards model with high-dimensional regressors

This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed to obtain useful statistical analyses. We study the partial least squares regression method. It turns out that it is naturally adapted to this setting via the so-called Krylov sequence. The resulting PLS estimator is shown to be consistent provided that the number of terms included is taken to be equal to the number of relevant components in the regression model. A standard PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to the well known primary biliary cirrhosis clinical data.