A Bühlmann Credibility Approach to Modeling Mortality Rates

In this article, we first propose a Bühlmann nonparametric credibility approach to forecasting mortality rates, and we then compare forecasting performances between the proposed Bühlmann approach and the Lee-Carter/Cairns-Blake-Dowd (CBD) models. Empirical results based on mortality data for both genders of Japan, the United Kingdom, and the United States with two age spans, a wide range of fitting year spans, and three forecasting periods show that the credibility approach contributes to much better forecasting performances measured by the mean absolute percentage error. Moreover, we give an informative credibility interpretation regarding the average decrements of an individual time trend for age x and a group time trend for all ages, and we discuss the effects of the slope and intercept of the linear functions for the forecasted mortality rates under the proposed Bühlmann nonparametric credibility approach and the Lee-Carter/CBD models. Finally, we also estimate the parameters of the Bühlmann credibility approach in a semiparametric framework, and we provide a stochastic version of forecasting mortality rates for the Bühlmann credibility approach.     

Incorporating the Bühlmann credibility into mortality models to improve forecasting performances

In this paper, we incorporate the Bühlmann credibility into three mortality models (the Lee–Carter model, the Cairns–Blake–Dowd model, and a linear relational model) to improve their forecasting performances, as measured by the MAPE (mean absolute percentage error), using mortality data for the UK. The results show that the MAPE reduction ratios for the three mortality models with the Bühlmann credibility are all significant. More importantly, the MAPEs under the three mortality models with the Bühlmann credibility are very close to each other for each age and forecast year. Thus, by incorporating the Bühlmann credibility we are able to converge the forecasting MAPEs resulting from the three different mortality models to a lower and more consistent level. Moreover, we provide a credibility interpretation with an individual time trend for age x and a group time trend for all ages. Finally, we apply the forecasted mortality rates both with and without the Bühlmann credibility to the net single premiums of life insurance products, and compare the corresponding MAPEs.     

A multi-dimensional Bühlmann credibility approach to modeling multi-population mortality rates

In this paper, we first propose a multi-dimensional Bühlmann credibility approach to forecasting mortality rates for multiple populations, and then compare forecasting performances among the proposed approach, the CBD model, the Lee-Carter model (LC), the joint-k (JoK-LC), the co-integrated (CoI-LC), and the augmented common factor (ACF-LC) Lee-Carter models for multiple populations. Mortality data from the Human Mortality Database are fitted to the underlying mortality models for both genders of three well-developed countries (the US, the UK, and Japan) and both genders of a developed country (France) and a developing country (Poland) with an age span 25–84 and a wide range of fitting year spans. Empirical illustrations show that the proposed multi-dimensional Bühlmann credibility approach contributes to more accurate forecast results, measured by AMAPE (average of mean absolute percentage errors over all fitting year spans), than the CBD, LC, JoK-LC, CoI-LC and ACF-LC models for three forecasting year spans 2004–2013 (10-year wide), 1994–2013 (20-year wide) and 1984–2013 (30-year wide).     

Zur Modellierung von Rückversicherungsverträgen in der dynamischen Finanzanalyse

In this paper we study the influence of Gaussian dependencies on the payoff of reinsurance contracts and the resulting effects on a non-life insurer's risk and return profile. To achieve this, we integrate different Gaussian dependencies and reinsurance contracts in a dynamic financial analysis (DFA) framework and conduct numerical tests within a simulation study. Depending on the reinsurance contract and the dependency employed, we find substantial differences in risk assessment for the ruin probability and for the expected policyholder deficit. The results have important implications for regulators and rating agencies that use these risk measures as a foundation for capital standards and ratings. Our results extend the findings of a recent working paper by Eling and Toplek (2008) with a detailed analysis of Gaussian dependencies under different reinsurance contracts.     

Risikomanagement bei der Professionalisierung des Frauenfußballs

Out of economic view sports are products, which compete with other leisure activities for different stakeholders (sportsmen, spectators, media and sponsor). To professionalize one kind of sport it is important to create a high (individual) utility for these four groups. It is shown, how with the help of a chronological model – called “chain of success” – by developing of the relations, network architectures can be established, which can help a kind of sport “to the break-through”. The risks arising with the professionalization are analyzed and the management of these risks is discussed. At the end we derive from the analysis a risk-management-manual for the professionalization of one kind of sport, which is applied to women's soccer in Germany, which wants to be established after large successes of the soccer clubs and national teams on a more professional level.     

Bayesian and Bühlmann credibility for phase-type distributions with a univariate risk parameter

Credibility theory is a statistical tool to calculate the premium for the next period based on past claims experience and the manual rate. Each contract is characterized by a risk parameter. A phase-type (or PH) random variable, which is defined as the time until absorption in a continuous-time Markov chain, is fully characterized by two sets of parameters from that Markov chain: the initial probability vector and transition intensity matrix. In this article, we identify an interpretable univariate risk parameter from amongst the many candidate parameters, by means of uniformization. The resulting density form is then expressed as an infinite mixture of Erlang distributions. These results are used to obtain a tractable likelihood function by a recursive formula. Then the best estimator for the next premium, i.e. the Bayesian premium, as well as its approximation by the Bühlmann credibility premium are calculated. Finally, actuarial calculations for the Bühlmann and Bayesian premiums are investigated in the context of a gamma prior, and illustrated by simulated data in a series of examples.     

Einfluß der Besteuerung in der wertorientierten Performancemessung im Kompositversicherungsunternehmen

The tax regulation framework is an important influence factor for value based management. So the implications of taxation on management decisions have to be explicitly verified and quantified within the valuation concepts. In this paper we take that point into account by extending the model for value based management of a composit-insurance company developed in the article from Schmautz and Hartung (ZVersWiss 98(4):411–430, 2009) by the framework of taxation. In the discussion we focus the effects of taxation and creation of provisions on the shareholder cashflow. Again the study examines theoretical aspects on the one hand and practical aspects with the special focus on an examplary implementation on the other hand.     

Chancen und Herausforderungen der Rückversicherung in der gesetzlichen Krankenversicherung

In 2009 a so-called morbidity orientated risk structure equalization scheme was installed for the German statutory health insurance in order to minimize structural differences between different providers with respect to revenue and expenditures. Even with this mechanism some risks to the individual health insurance providers remain. Reinsurance could be a way to mitigate these risks, but so far only very few contracts have been signed. Moreover the existing reinsurance contracts only focus on the periphery of the statutory health insurance system such as travel health insurance. In this article we therefore analyse existing risks for individual health insurance providers and evaluate their (re-)insurability. Hereafter the potential for reinsurance solutions in the German statutory health insurance itself as well as in newer forms of healthcare provision (e.g. integrated health care and managed care) is discussed. We find that reinsurance may be a reasonable solution for many of the risks in the statutory health insurance scheme. But as research in this area is very young further analysis of the nature of risks is necessary.     

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.     

über die Entwicklung der Erneuerungsfunktion in eine Potenzreihe

Abstract

In einer Personengesamtheit soll das Ausscheiden von Personen infolge Todesfall kompensiert werden durch Neuzutritte gleichaltriger Personen, sodass der Umfang der Gesamtheitkonstant bleibt.     

Zur Entscheidungsnützlichkeit eines IFRS-Abschlusses von Versicherern – Analyse der angedachten Regelungen zum endgültigen IFRS 4

In its Discussion Paper from May 2007 for the final IFRS 4 (“Insurance Contracts”), the IASB planned the “Current Exit Value” (CEV) to evaluate insurance liabilities. The aim of this article is to examine the impacts of the planned Current-Exit-Value-Approach on the decision usefulness of insurers' financial statements. In order to evaluate accounting rules, the criterion decision usefulness is divided into two sub-criteria – relevance and reliability. We found out that the Current-Exit-Value-Approach for insurance contracts in conjunction with fair value accounting of relating assets actually generates relevant information for users of insurers' financial statements. But we have serious concerns about a cost-adequate implementation of CEV approach. Furthermore, the reliability of accounting information based on a synthetic fair value is strongly questionable. Only extensive disclosure requirements can bring transparency to users and therefore assure reliable accounting information. Besides, there are other topics that should be reviewed before releasing a final standard (e.?g. customer relationship, credit characteristics of insurance liabilities, unit of account).     

Das Restglied der Taylorschen Reihe des Rentenbarwertes und einige Formeln des Zinsfussproblems für grosse Zinsspannungen

Abstract

Im Zinsfussproblem spielen eine wichtige Rolle drei Hilfsfunktionen der Summen der diskontierten Zahlen, die wir vorweg kurz erwahnen wollen. Unter der nten Summe der diskontierten Zahlen D_x verstehen wir SpezieU haben wir:      

Ursachen geschlechtsspezifischer Kostenunterschiede in der Privaten Krankenversicherung: Eine empirische Untersuchung unter besonderer Berücksichtigung der Anforderungen des AGG

The new “Allgemeine Gleichbehandlungsgesetz” (General Equal Treatment Act) also influences the premium calculation of the German Private Health Insurance to antagonize gender discrimination in premiums. The higher premiums in the Private Health Insurance women pay are caused by higher expectation of life, by the risk of fertility, and by higher individual health-care costs for health services. We study how strong the gender influence in health-care costs of men and women are and if they are influenced by the factors mentioned above. We analyse if there is any gender discrimination in premium calculation in the Private Health Insurance. The results show that after eliminating the factors only a small reduction of premiums is found. We still find a cost difference between women and men. This difference can be explained by the different usage of health services but this depends less on the gender rather on individual psychosocial factors.     

Industrieversicherung in der Türkei im Vergleich zu Deutschland

In conjunction with the rapidly advancing industrialization of Turkey, the segment of industrial insurance has also steadily gained in importance. People seeking cover for industrial risks situated in Turkey, however, face several rather significant constrictions. Whilst some of those may be circumvented at least partially, the Turkish situation raises the question of the need for legislative reform (possibly inspired by German law) in this area. Such would foster the development of more innovative and adequate insurance products by the Turkish insurance market.     

Naturgefahrenmodellierung in internen Risikomodellen – Unverzichtbares Rüstzeug für Strategieentscheidungen des Managements der Zukunft

Management requires internal models, which will usually span a period of several years (such as five), for analysing the financial situation of the insurance company and supporting strategic value- and risk-based company management. Catastrophe risks play an important role in risk management as a substantial share of the company’s entire risk capital is committed to natural catastrophes. So the article aims to compare two approaches in modelling storm loss in the context of applicability in strategic management. Concretely modelling deductibles in storm insurance is shown using the mathematical statistical approach. A case study will analyse various strategies and their effects on the insurance company’s single and multi-year risk-return position using example data where risk is dominated by catastrophes in order to give a concrete idea for the use of multi-period internal models in the context of management.     

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.     

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.