Prämienkalkulation und die „Sanierung“ von Versicherungsverträgen

For assessing the risk adjusted insurance premiums, we always face the challenge that we don’t know the respective distribution functions of the probable claims and the probability of occurrence. Purely chance-based deviations from expected damages are no sufficient reason for premium increases. This means that for preparing for such deviations we have to distinct between chance-based and other deviations from expected and realised damage events. For adjusting insurance contracts due to new information, there are three possible strategies: first, we could ignore the past premium and calculate them based on the new data sample. Alternatively we could make use of a Bayesian learning process, which means to adjust the past premiums by taking into account the new information. The third strategy refers to a statistical test of hypotheses. This means to only adjust a premium if the original assumptions on the possible distribution of claims have to be rejected statistically. Looking at the certainty of the contracts and a steady calculation basis, there are many reasons in favour of the statistical test of hypotheses. The stringent usage of this method can lead to a sound basis for negotiations between insurance provider and holder. The improvement of transparency of taken risks is regulatorily desirable as well as helpful for evaluation of solvency.     

Eine graphische Darstellung der Leibrente,der einmaligen Prämie,der Jahresprämie und der Prämienreserve

Abstract

Um eine graphische Darstellung einer gegebenen, eindeutigen Funktion f(α) zu erhalten. denken wir uns die den Wert en α′, α″,… α_n der unabhängigen Veränderlichen entsprechenden Grössen x = l . f(α) als Abszissen auf eine Gerade von demselben Ausgangspunkt abgetragen und bezeichnen dann die Endpunkte der Abszissen mit dem zugehörigen Wert von α. Öber die Konstante l, den Modul, können wir frei verfügen und hierdurch einen passenden Massstab erhalten.     

Eine methode zur Berechnung von Alters- und Invaliditätsrenten bei willkürlicher jährlicher Prämienzahlung

Abstract

Die sehwedische staatliche Pensionsversicherung ist bekanntlich als eine kombinierte Alters- und Invaliditätsversieherung organisiert. Mit 67 Jahren oder bei früher eingetretener Invalidität fängt die Auszahlung einer Pension an, deren Betrag sich als ein gewisses Prozent der einbezahlten Prämien ergiebt, für Manner 30 und für Frauen 24 Prozent. Diese Höchsbeträge werden jedoch für diejenigen Personen, die bei dem Inkrafttreten des Alterspensionsgesetzes eine gewisse Altersgrenze überschritten hatten, einigermassen modifiziert.     

Prämienanpassungen im Risikoklassenmodell der Privaten Krankenversicherung

In Zähle (Blätter DGVFM 31:39–64, 2010), a risk class model for the portability of the reserves for increasing age in Germany’s private health insurance system was introduced. In the present article, this model is extended in such a way that also successive premium adjustments are taken into account. In our model, the current risk class of an insurant does not play any role for a premium adjustment. In fact, only the risk class, to which the insurant belonged at the beginning of the contract, matters for a premium adjustment. From a mathematical point of view, our model provides a neat solution for the problem of the portability of the reserves for increasing age. In particular, the presented model is a real extension of the conventional model of Germany’s private health insurance system insofar as the conventional model can be recovered by restricting to a single risk class. So the well-tried premium calculation principle will basically remain.     

Über periodische und angenäherte Beharrungszustände

Man stösst in den verschiedensten Zweigen der angewandten Mathematik — so in der Statistik, in der Versicherungstechnik, in der Physik, u.s.w. — sehr oft auf die Berechnung von Grössen, die als durch einen fortlaufenden Zugang irgend eines erzeugenden Elementes, deren Wirkung auf die zu studierende Grösse auf eine bestimmte Zeitdauer begrentzt ist, aufgebaut angesehen werden können.     

Aufsichtsrats- bzw. Diversitätsmerkmale und Profitabilität von deutschen und österreichischen Versicherungsunternehmen

This paper focuses on supervisory boards and investigates various board characteristics for the largest German and Austrian insurance companies. Furthermore, the study examines the link between diversity policies and financial performance.The study reveals some differences between the two aforementioned countries, which are mainly driven by size effects. In addition, the analysis shows that larger and stock listed insurance companies have better diversity management policies and a higher proportion of female directors. There is no significant correlation between gender diversity measures and profitability.     

Die Lebensversicherung mit exponentiell ansteigender Prämienreserve (Sparversicherung)

Abstract

Die gebräuchlichste Form der Lebensversicherung ist heute die Kapitalversicherung auf den Todes- und Erlebensfall. Bei ihr wird im Versicherungsfall ein bestimmtes Kapital fällig; als Gegenleistung sind hierfür vom Versicherungsnehmer laufend Prämien zu entrichten in Form von gleichen Jahresbeträgen oder auch gleichen unterjährigen Raten. Dieses Prinzip, einem gleichmässigen Versicherungsschutz einerseits gleichmässig fällig werdende Prämien gleicher Höhe andererseits gegenüberzustellen, wird durch die ausgleichend wirkende Funktion der Prämionreserve möglich, welche die bisher nicht benötigten Teile (Sparprämien) der eingezahlten Prämien jeweils reserviert für die sich zukünftig durch Tad oder Ablauf mehr und mehr häufenden Versicherungsfälle. Damit erfüllt die Prämionrosorve als Regulator eine wichtige versicherungstechnische Aufgabe. Dennoch bleibt sie dem Versicherungsnehmer im allgemeinen unbekannt, weil ihre jeweilige Hohe nur mit Hilfe von umfangreichen Tabellen nach mathematischen Formeln berechnet werden kann, so dass ihr verschwiegenes Dasein nicht selten zu Missverständnissen Anlass gibt.     

Beitragsentwicklung und Verteilungseffekte der RfB in PKV-Beständen

The possibility of adjusting premiums is a characteristic feature of the german Private Health Insurance (PKV), which is even required by german law. The main reason for increasing premiums lies in the rise of claims and corresponding compensations. Therefore, the time development of health care costs is of primary importance for the PKV. In the present article, various models for the future evolution of age-specific health care expenditure are studied with respect to their effects on the premiums’ dynamic and policyholder participation. In particular, it is analysed how the age-specific cohorts participate in the benefits.     

Telemedizin – Angebote,Chancen und Kosteneffektivität

Digitalisation of the health care system proceeds. Therefore it is to be expected that telemedicine applications will also be introduced into health care. Currently, the number of telemedicine applications in Germany is low and it is also scarce in comparison to foreign countries. This is striking because it is usually supposed that telemedicine applications have got a great potential to improve health care and reduce expenditures. Hence, this publication discusses offers, chances and the cost-effectiveness of telemedicine.     

Determinanten der Liquidität in der deutschen Schaden- und Unfallversicherungsindustrie: Bedeutung,Erklärungskraft und Auswirkung der Finanzkrise

The aim of this paper is to analyze the corporate liquidity and its determinants for the German property-liability insurance industry using company-level data for the period 2002–2014. We first investigate the differences in cash holdings across insurers. We then quantify the relative importance of firm-level determinants compared with macroeconomic determinants in explaining insurers’ cash holding choices. In addition, we examine whether the financial crisis of 2008 has an impact on the liquidity situation of insurers. Our results indicate that cash holdings vary significantly across German property-liability insurers. The firm-level determinants size, group affiliation and reinsurance utilization explain more than 50% of the variation. We also find that macroeconomic conditions appear to have negligible effects on the liquidity situation of insurers. In addition, we do not find evidence that the liquidity of German property-liability insurers is influenced by the financial crisis of 2008. The proportion of cash remains relatively stable at 6% of the total assets.     

Über den Einfluss einer Änderung der Sterblichkeit auf die Prämienreserve

Abstract

In einer Note über die Theorie des Deekungskapitales habe ieh für das reduzierte Kapital der gemisehten Versicherung auf die Beträge At den Ausdruck gebraueht (1) wobei als Deckungsintensität bezeichnet wurde.     

Erklärung der privaten Krankenversicherungsnachfrage anhand ökonomischer und psychologischer Einflussfaktoren

To be able to plan measures insales planning successfully, informations are necessary about the expected trend of demand in the future. In this respecttheoretical funded andempirical relevant correlations between exogenous influencing factors and the process of demand must be systematically explored. Consequently for the private health insurance aglobal model was developed, which is the basis for presenting exemplarily an approach of explanation for the health cost insurance. Via this approach theshort-term fluctuations in the trend of demand, which were noticed in the past, can be traced satisfactorily. In this context besideseconomical alsopsychological influences like attitudes and expectations must be explicitly integrated in the approach of explanation. Naturally also the effects ofsociopolitical events, which are relevant to demand, were included in the analysis, especially as the process of demand for private health insurance is substantially marked by sociopolitical legislation.     

Ökonomische Aspekte der Entlohnung und Regulierung unabhängiger Versicherungsvermittler

The compensation and regulation of independent intermediaries is an important issue in insurance markets. With this respect, the profitability and importance of fee-for-service and commission compensation of intermediaries is lively discussed in academia and in the insurance industry. This paper summarizes economic rationales why and in which lines of business insurance companies sell their products via independent intermediaries. With this respect, it is analyzed how different forms of compensation affect important market functions of independent intermediaries. Finally, the economic impact of certain regulatory interventions, like a mandatory disclosure or a general ban of any commissions and the German ban for intermediaries to share commission with policyholders, on market efficiency is discussed.     

Das Dreiecksverhältnis zwischen Versicherer,Versicherungsnehmer und versicherten Personen in Innenhaftungsfällen der D&;O-Versicherung

The article deals with the rights and obligations between the policyholder, the insured directors and officers of the policyholder and the insurer in ‘Insured vs. Insured’ D&;O claims. Based on a case study where several directors commit wrongful acts the following questions will be examined: (1) whether or not the policyholder is entitled to directly claim damages from the insurer, (2) whether or not the policyholder violates its duties towards the insurer or the insured directors by its deliberate choice not to make claims against all insured at the same time but in different policy periods, and (3) which obligations has the policyholder towards its directors when there is not sufficient coverage to cover all claims of the policyholder against the directors.     

Garantieversprechen für Gebrauchsgüter als erlaubnispflichtige Versicherungsgeschäfte aus deutscher und europäischer Sicht

The article deals with the conditions under which the provider of guarantees for consumer goods operates an insurance business and therefore needs a permit. This question is of fundamental academic importance as it concerns the limits of insurance. Secondly, it is of practical relevance, as is reflected in court decisions in Germany as well as in other European countries. A comparative analysis supports the following rules: An extension of the statutory warranty offered by the seller or manufacturer is normally to be regarded as ancillary to the purchase agreement, which does not lead to regulatory licensing requirements. By contrast, if a third party offers a guarantee this is to be considered as an insurance business and therefore requires a permit.     

Die Aufdeckung des tatsächlichen Schädigungspotentials eines versicherten Risikos und das Institut der Gefahrerhöhung

Against the background of the rapid spread of new technologies such as nanotechnology to name only one, third party insurers are faced with a multitude of challenges. The reason for this is the typically totally unknown damage and thus liability potential of these technologies. In this context special focus is on the aggravation of risk and the question whether the rights included in §§ 24 f. of the German Insurance Contract Act should be granted to the insurers in the event of any future revelation of the actual damage potential. This must, however, be answered in the negative since here only the risk of an initial and not the risk of a subsequent disruption of the equivalence mandate as assigned to the insured as per §§ 23 ff. of the German Insurance Contract Act applies.     

Grundfragen zu Anzeige-, Auskunfts- und Aufklärungsobliegenheiten nach dem VVG 2008

This article analyzes the disputed legal nature of the duty to notify and the duty to disclose information according to sections 30 et seq. of the German Insurance Contract Act (VVG). To the extent to which the aforementioned legal provisions impose such obligations on a third party, the author reaches the conclusion that they are to be regarded as true legal obligations, i.e. their breach may result in damage claims. As to the policyholder, however, the legal provisions must be qualified as statutory warranties (so-called Obliegenheiten) without sanctions. Therefore, in order to sanction a policyholder’s breach of his obligations, the contracting parties have to turn the statutory Obliegenheiten into contractual Obliegenheiten, which are then subject to section 28 VVG. In the second part of the article the author addresses the scope of application and the content of the Obliegenheit to instruct the policyholder according to section 28 subsection 4 VVG. This Obliegenheit is imposed on the insurer as a requirement for the sanction of a breach of the contractual duties to provide information and to disclose by the policyholder.