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We consider a contingent claim model framework for participating life insurance contracts and assume a competitive market with minimum solvency requirements as provided by Solvency II. In a first step, the implications of the regulator's imposing a particular interest rate guarantee on the insurer's asset allocation are analyzed in a reference situation. We study the sensitivity of the interaction between the interest rate guarantee and the asset allocation when the risk-free interest rate changes. Particular attention is paid to the current market situation where the guaranteed interest rate is often close to the risk-free interest rate. In a second step, we assess at what level the interest rate guarantee should be set by the regulator in order to maximize policyholders' utility. We show that the results yielded by the proposed concept to derive an optimal value for the interest rate guarantee are very stable for various model parameters. IntroductionA minimum interest rate guarantee and participation in the annual return of the insurance company's asset portfolio are the two core components in traditional endowment contracts most popular in the German-speaking countries. Both elements are offered in so-called participating life insurance contracts and are in general regulated by the insurance supervisory authority. In current contracts offered, minimum interest rate guarantees are based on the savings premium and usually provided on a year-by-year basis (cliquet-style) for the whole contract duration. Contracts often have a very long duration with savings accumulation periods of over 40 years. 1 In view of (higher) equity capital requirements under new solvency regulations (see, e.g., Solvency II in

In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. This paper provides proofs of the results published earlier (see C. R. Acad. Sci. Paris, Ser. I 337 (2003) 679-684), gives a generalization of the latter to more than two domains and contains extensive numerical illustrations. New results including the spectral analysis of the iteration operator and a numerical method to evaluate the constant of the strengthened Cauchy-Buniakowski-Schwarz inequality are presented. Mathematics Subject Classifications (1991) 65N55 · 65N30 · 65N12

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Due to the demographic changes and population aging occurring in many countries, the financing of long-term care (LTC) poses a systemic threat. The scarcity of knowledge about the probability of an elderly person needing help with activities of daily living has hindered the development of insurance solutions that complement existing social systems. In this paper, we consider two models: a frailty level model that studies the evolution of a dependent person through mild, moderate and severe dependency states to death and a type of care model that distinguishes between care received at home and care received in an institution. We develop and interpret the expressions for the state-and time-dependent transition probabilities in a semi-Markov framework. Then, we empirically assess these probabilities using a novel longitudinal dataset covering all LTC needs in Switzerland over a 20-year period. As a key result, we are the first to derive dependence probability tables by acuity level, gender and age for the Swiss population. We find that the transition probabilities differ significantly by gender, age and time spent in the frailty level and type of care states.

Pharmaceutical and non-pharmaceutical interventions (NPIs) have been crucial for controlling COVID-19. They are complemented by voluntary health-protective behavior, building a complex interplay between risk perception, behavior, and disease spread. We studied how voluntary health-protective behavior and vaccination willingness impact the long-term dynamics. We analyzed how different levels of mandatory NPIs determine how individuals use their leeway for voluntary actions. If mandatory NPIs are too weak, COVID-19 incidence will surge, implying high morbidity and mortality before individuals react; if they are too strong, one expects a rebound wave once restrictions are lifted, challenging the transition to endemicity. Conversely, moderate mandatory NPIs give individuals time and room to adapt their level of caution, mitigating disease spread effectively. When complemented with high vaccination rates, this also offers a robust way to limit the impacts of the Omicron variant of concern. Altogether, our work highlights the importance of appropriate mandatory NPIs to maximise the impact of individual voluntary actions in pandemic control.

Purpose Over the last decade, technological and social trends have significantly influenced the relationship between customers and insurers. New buying patterns, price comparison platforms and the usage of different interaction channels driving single-product purchases and impacting lapses have influenced insurers’ customer portfolios and development. The purpose of this paper is to study the features driving the customer relationship along three areas, namely, customer acquisition, development and retention. Design/methodology/approach After defining 14 related hypotheses, the authors use econometric analyses to quantitatively support these hypotheses in the three areas of interest. The authors build on a large-scale longitudinal data set from a Swiss insurance company covering the period from 2005 to 2014 and including 2,757,000 customer-years. The data comprise information on private customers, their contract history, including coverage and losses and the channels used for buying insurance. This analysis focuses on the two most common non-life insurance products, namely, household/liability and car insurance. Findings The authors provide descriptive statistics and results from econometric analyses to determine the significant features and patterns affecting customer development and retention. Among the main results, the authors underline the significant influence on cross-selling given by the customer’s age and the interaction channel. Customers from rural regions are more loyal and likely to conduct cross-buying when compared to their peers from urban regions. Car insurance holders are more likely to lapse than household/liability insurance clients. Finally, while newly acquired customers tend to buy only a single product, the authors show the importance of cross-selling for retaining customers. In fact, customer retention is positively influenced by the number of products hold. Research limitations/implications This work is relevant for academics and practitioners alike, adding a quantitative basis to the understanding of managing customer relationships and for the development of further prospective models. Further work could investigate or add products, extend the study to other companies and focus on customer development with time. Originality/value This study explores a large-scale longitudinal data set. The analyses of customer acquisition, development and retention can support insurers to construct their own models for customer relationship management.

This article uses cross-sectional data from the Survey of Health, Ageing, and Retirement in Europe (SHARE) database to test the effect of both long-term care (LTC) public benefits and insurance on the receipt of informal care provided by family members living outside the household in Italy and Spain. The choice of Italy and Spain comes from the fact that informal care is rather similar in these two countries while their respective public LTC financing systems are different. Our results support the hypothesis of LTC public support decreasing the receipt of informal care for Spain while reject it for Italy. They tend to confirm that the effect of public benefits on informal care depends on the typology of public coverage for LTC whereby access to proportional benefits negatively influences informal care receipt while access to cash benefits exerts a positive effect. Our results also suggest that private LTC insurance complements the public LTC financing system in place.