Ein konvergenzkriterium für erneuerungszahlen

Abstract

Inhalt des bekannten Erneuerungsproblems ist es, bei einer Gesamtheit (Versichertenbestand, Viehherde, Warenlager, etc.) deren Elemente infolge gewisser Ursachen (Todesfall, Unbrauchbar-oder Verkauft werden, etc.) aus der Gesamtheit ausscheiden können, den Neuzugang zu untersuchen, der dazu nötig ist, die Gesamtheit auf konstantem Umfang zu erhalten. Bei diskontinuierlich sich erneuernden Gesamtheiten, wie sie in dieser Note betrachtet werden sollen, vollziehen sich die Wechsel im Bestand immer am Ende einer festen Zeiteinheit (Jahr, Tag, etc.). Das zufallsartige Ausscheiden der Elemente aus der Gesamtheit sei geregelt durch ein als bekannt vorausgesetztes Abbaugesctz. Darunter versteht man ein System von K - 1 Zahlen (1) P ₀, P ₁, P ₂, . . PK;wo P _v die Wahrscheinlichkeit für ein der Gesamtheit neu angegliedertes Element ist, ihr mindestens v Zeiteinheiten anzugehören.Diese Wahrscheinlichkeiten können durch überwachungeiner geschlossenen Elementengesamtheit statistisch gewonnen werden. Das Abbrechen des Abbaugesetzes bedeutet, dass kein Element mehr als K Zeiteinheiten der Gesamtheit angehört.     

Ein Reservierungsverfahren für die Rechtsschutzversicherung nach Art der Lebensversicherung

In this paper we introduce a new approach to the calculation of claims reserves (known and IBNR cases) which is particularly adapted to the business model of legal expense insurance. An essential aspect here is the split into two model components: case numbers and average claim costs. In contrast to other reserving methods for case numbers and claims cash flows which are frequently used in practice without checking the validity for application we introduce a model in which the time until case settlement is described by a lifetime distribution according to the principles of life insurance. The split of model components also allows for a simple implementation of cost inflation effects which is required by German law. Finally, the approach proposed here can readily be transferred to the calculation of IBNR reserves.     

Die stochastische Modellierung von Großschäden für den Einsatz in internen Risikomodellen der Schadenversicherung

Along with individual corporate management and regulatory matters for instance within EU regime Solvency II, Internal Risk Models are very important for major general insurance companies. Of crucial importance in building these internal models, is the stochastic modelling of large claims and in particular, the selection and parameterization of suitable probability distributions for the amount and number of claims based on empirical data. To this end, in practice, a visually-based methodology is more appropriate and workable than strict mathematical approaches. Based on a practical case study, this paper provides some insight into a visually-based methodology for internal risk models.     

Aus der Sterblichkeitserfahrung einer Heilanstalt für Lungenschwindsüchtige

Abstract

Die im folgenden angegebenen Zahlen sind aus dem in dem Sanatorium Takaharju (Finnland) während der 20-jährigen Periode 1903–1923 angesammelten Material hergeleitet worden. Das Sanatorium ist eine Heilanstalt nur für Lungenschwindsüchtige.     

Unterschriftenpads in der Kranken- und Lebensversicherung – Zur Vereinbarkeit der Verwendung eigenhändig unterzeichneter elektronischer Dokumente mit den Formvorschriften für den Vertragsabschluss in der Kranken- und Lebensversicherung

Insurance business is more and more based upon ecommerce and internet. But this situation causes legal problems. Insurance regulations are often based on the obligation to close contracts or to submit documents in a written form. This obligation prevents insurance business from using new modern tools like for instance PADs and tablet computers for the transmission of consumer data to the IT center of an insurance company. The following considerations deal with the use of tablet PCs and internet in life and health insurance business and tries to demonstrate that the written form required by law is not a real obstacle in insurance business.     

Aufsichtsrechtliche Rahmenbedingungen für die Tätigkeit von EU-Versicherern in der Türkei

In recent years the Turkish insurance market has exerted a strong appeal, especially for insurers seated in the EU, in view of its exponential growth rates and its dormant growth potential. EU insurers are, however, subject to more stringent insurance supervisory requirements when entering this insurance market, external to the EU, than when expending into other European insurance markets.     

Die Bedeutung der Haftpflichtversicherung für die Annahme konkludenter Haftungsausschlüsse

The article covers the practically important question under which circumstances the construction of implied exclusions of liability is influenced by the liability insurance of the injuring party. It is focused on the two practically most relevant case groups in which the jurisdiction considers implied exclusions of liability possible (liability in accommodation agreements and liability in sports). The author firstly shows that under tort law, the consideration of liability insurance is both possible and necessary. Secondly, the author demonstrates that possible objections based in insurance law (such as the principle of separation) are not convincing. This is not limited to compulsory insurances, but applies to all types of liability insurances.     

Schöpft die PKV den Rahm ab? Eine spieltheoretische Analyse der Effekte der PKV auf die Medikamentenqualität

Quality of medical treatment is a major goal of Germany’s statutory health insurance system. According to our game theoretic approach, existing price-discrimination between statutory and private health insurance leads to higher quality of innovative drugs. Hence, a move into the direction of a national health service system (so-called citizen insurance) should result in a reduction of innovative drugs’ quality. Moreover and in the case of citizens insurance’s implementation, innovative drugs’ price level should increase for patients with statutory health insurance. Furthermore, a similar effect is caused by the Act on the Reform of the Market for Medicinal Products (AMNOG) which leads to reduced prospects for pricediscriminations between the statutory and private health insurance system. In summary, the existence of private health insurance in Germany does not cause unfavourable cream-skimming. Rather the split-up of the German health care sector (statutory vs. private health insurance) results in eligible higher drug quality at lower prices for patients with statutory health insurance.     

Das Hamburger Beihilfemodell – Ein Vergleich der internen Renditen von GKV und PKV

At the beginning of their career civil servants in Germany can choose between the social health insurance system and a private plan combined with a direct reimbursement of the government up to 80%. Most civil servants chose the latter, also because they have to cover all contribution payments to the social system themselves, while normal employees get nearly 50% from their employers. The state of Hamburg decided to change the system by paying a share of the contributions if civil servants choose the social plan. Using a comparison of internal rates of return in both schemes, we show that this celebrated reform will not change the decision calculus for the average civil servant household and will probably thereby increase the adverse selection of high risk cases towards the social health insurance.     

Neue Sterblichkeitstafeln der “Varma” für minderwertige Leben

Abstract

Die in der Versicherung minderwertiger Leben angewendeten hypothetischen Sterblichkeitstafeln zerfallen ihrem Klassifizierungsgrunde nach in zwei Gruppen: die Klassifizierung gründet sich 1:0 auf die Art der Minderwertigkeitsursache, 2:0 auf den geschatzten Grad der Minderwertigkeit.     

Geologisches Risikomanagement für Versicherungen

The application of Geoinformationsystems under geological, hydrological and hydrogeological aspects for the risk management is a further development of the geographical underwriting of the insurance industry. The knowledge of the geology, hydrology and hydrogeology is fundamental for the understanding and spatial analysis of insured objects before and during loss events for example with contaminations of the aquifer. Furthermore possible loss scenarios could be prevented or minimized if the subsurface geology and hydrogeology are already known and integrated in the initial insurance appraisal. The modelling and classification of the geoscientific knowledge also enables the definition of Action Zones, which allow a better appraisal and assessment of the insurable objects. This leads to an optimized and transparent premium calculation for both, the insurance and the policyholder (Münchener Rück 2002). The visualization of the geoscientific subsurface information in Geoinformationsystems is simple and economical feasible, it is quick to analyze and combinable with additional information and gives important insights in the subsurface structures. The paper describes a workflow how such Action Zones could be assessed and the additional information for the premium is generated.     

Betriebswirtschaftliche Rahmenbedingungen für eine nachhaltige Entwicklung von „New Economy-Unternehmen” in der Versicherungswirtschaft

While a whole set of ?new economy enterprises” in the insurance business were successfull, many of them left the market after a very short life span. What are the substantial conditions for the success of these enterprises? The answer to this analisis can be summarized in three aspects:

1. The business model should contain a sufficient information-economic transaction benefit.
2. The branding strategy should create in the sense of Informationssurrogates sufficient confidence and generate respectable traffic.
3. The supply of sufficient investment capital must be guaranteed during the entire starting period.

     

Ein versicherungsmathematischer Ansatz zur Berechnung von Marktwerten der Deckungsrückstellung in der Lebensversicherung

Based on well-known actuarial calculation principles for the determination of the liabilities for life insurance contracts, we present a method for the calculation of fair values of liabilities. This method is consistent with the Solvency II requirements. The main principle is the discounting of probability weighted future cash flows, including assumptions on interest rates, costs and lapse for the calculation of actuarial present values. In addition to the mathematical framework, we discuss some numerical results that compare the traditional liabilities with the fair value approach. The presented principles are also relevant for the IFRS directives, which are at the moment available as exposure draft.     

Verfassungsrechtliche Vorgaben für Sozialversicherungsreformen

German social insurance is to adapt to societal changes and requires reforms if it is not to fail in its protective purpose. The Constitution sets framework conditions for such reforms: It allows for further development and changes in existing structures, yet it also postulates consistency, protects acquired rights and urges existing social security systems to be effective. The legislator may not completely dispense with risk protection. At the same time, the Constitution grants the legislator sufficient scope for action, since he may lay down the type and level of security. However, the Constitution also ensures a certain continuity through the protection of confidence, as drastic restructuring measures may entail great costs with respect to the transition of protected rights.     

Zur Variationsrechnung für die Verteilungsfunktionen

Abstract

Die Variationsrechnung hat zur Aufgabe, unter den Funktionen F(x), die einer gewissen Klasse C angehören, diejenige zu finden, welche ein Funktional J[F] zum Maximum oder Minimum macht. In der allgemeinen Variationsrechnung enthält die Definition der Klasse C gewöhnlich nur derartige Bedingungen, die erforderlich sind, urn die Existenz von J[F] zu sichern, z. B. Kontinuität oder Differentierbarkeit bis zu einer gewissen Ordnung, und ausserdem eventuell gewisse “Nebenbedingungen” von der Form J_v [F] = c_v (v = 0, 1, ..., n).     

Katastrophenanleihen als Risikotransfer-Instrument für Industrieunternehmen

All over the world an increase in natural catastrophes and resulting damages can be observed for entire economies as well as for individual industrial enterprises. This trend leads to extraordinary expensive traditional natural catastrophe insurance or even a lack of insurance capacities. Due to the increased threat resulting from natural catastrophes and the inefficiencies of traditional insurance solutions, it will be analyzed in the following whether catastrophe bonds (cat bonds), as an alternative risk transfer instrument, should play a role in the risk management portfolio of industrial companies. It will be discussed whether catastrophe bonds are possible risk transfer instruments for industrial companies and whether certain basic prerequisites for a confirmation of the suitability are recognizable. In a further step, the design possibilities for cat bonds will be presented and the most suitable design alternatives for industrial companies as issuers of cat bonds will be elaborated. In addition, a critical comparison between the usage of traditional insurance solutions and cat bonds by industrial companies in order to protect themselves against natural catastrophes will be conducted. The result is a first orientation and a general guideline for dealing with catastrophe bonds as part of the operational risk management for industrial companies.     

Ausgleichung der Sterblichkeit der Versicherten in der schwedischen lebensversicherungsanstalt “Trygg” für die Periode 1899–1916 (Volksversicherung)

Abstract

Die vorliegende Ausgleichung der Sterblichkeit in der “Trygg” ist von mir im ersten Halbjahr 1921 im Auftrag des Kgl. Schwedischen Aufsichtsamts für Privatversicherung vorgenommen worden.     

Pay-As-You-Drive Angebote von Erstversicherern für Privatkunden

“Pay-as-you-drive” (PAYD) concepts for car liability insurances envisage that real driving behavior and situation data are captured and processed via car sensors and tracking systems in order to calculate case-specific insurance rates which better correspond to the risk profiles of policy holders (PH) than conventional tariffs. The present article provides an outline of PAYD insurance variants, of legal arrangements with particular relevance for PAYD offerings in Germany and of the international dissemination of PAYD concepts. It shows that although PAYD offerings of direct insurers (DI) for private customers are not barred by insurmountable technical or legal barriers, they so far have little practical relevance in Germany. Against this background expected PAYD impacts on revenues and costs of DI are discussed in detail in order to analyze the extent to which DIs’ cautious PAYD offering strategies may be qualified as economically reasonable. The investigation suggests that the profitability effects of PAYD insurances of DI targeted at private customers are far from being definitely and clearly positive. Thus, it is very unlikely that DI will make significant investments on their own in order to create a large German residential market for PAYD insurances. Rather such a market will not emerge without accompanying state interventions.