Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors

The present paper proposes a new methodology to model the lapse risk in life insurance by integrating the dynamic aspects of policyholders’ behaviors and the dependency of the lapse intensity on macroeconomic conditions. Our approach, suitable to stable economic regimes as well as stress scenarios, introduces a mathematical framework where the lapse intensity follows a dynamic contagion process, see Dassios and Zhao (2011). This allows to capture both contagion and correlation potentially arising among insureds’ behaviors. In this framework, an external market driven jump component drives the lapse intensity process depending on the interest rate trajectory: when the spread between the market interest rates and the contractual crediting rate crosses a given threshold, the insurer is likely to experience more surrenders. A log-normal dynamic for the forward rates is introduced to build trajectories of an observable market variable and mimic the effect of a macroeconomic triggering event based on interest rates on the lapse intensity. Contrary to previous works, our shot-noise intensity is not constant and the resulting intensity process is not Markovian. Closed-form expressions and analytic sensitivities for the moments of the lapse intensity are provided, showing how lapses can be affected by massive copycat behaviors. Further analyses are then conducted to illustrate how the mean risk varies depending on the model’s parameters, while a simulation study compares our results with those obtained using standard practices. The numerical outputs highlight a potential misestimation of the expected number of lapses under extreme scenarios when using classical stress testing methodologies.     

Dynamic hybrid products with guarantees—An optimal portfolio framework

Dynamic hybrid products are pension products that consist of a dynamic combination of classical with profits participating life insurance contracts (or a bank account) and fund savings plans. To put such products in an optimal utility framework, we derive an optimal combination of a money market account, a CPPI-style fund and a free fund in continuous trading via transforming the original investment problem into a conventional portfolio problem in the presence of a guarantee condition. By this, we obtain (semi-) explicit forms of the dynamic weights for the different ingredients of a dynamic hybrid product.     

Analyzing legal regulations in the Norwegian life insurance business using a multistage asset–liability management model

The legal regulations for the life insurance business in Norway have recently been, and still are, under revision. The government's intention is to secure the interests of the customers in life insurance companies. However, there has been debate as to whether the regulations really are in the customers' best interest. We apply an asset–liability management (ALM) model to analyze the implications of the regulations. The model is multistage, stochastic and integrates assets and liabilities. We employ a four stage model to analyze the legal regulations, and conclude that the current legal framework is not in the insurance holders' best interests.     

Two applications of Brouwer’s fixed point theorem: in insurance and in biology models

In the first part of the article, a new interesting system of difference equations is introduced. It is developed for re-rating purposes in general insurance. A nonlinear transformation φ of a d-dimensional (d ≥ 2) Euclidean space is introduced that enables us to express the system in the form f^t+1:=φ( f^t), t = 0, 1, 2,. …. Under typical actuarial assumptions, existence of solutions of that system is proven by means of Brouwer’s fixed point theorem in normed spaces. In addition, conditions that guarantee uniqueness of a solution are given. The second, smaller part of the article is about Leslie–Gower’s system of d ≥ 2 difference equations. We focus on the system that satisfies conditions consistent with weak inter-specific competition. We prove existence and uniqueness of the equilibrium of the model under surprisingly simple and very general conditions. Even though the two parts of this article have applications in two different sciences, they are connected with similar mathematics, in particular by our use of Brouwer’s fixed point theorem.     

An analysis of transaction costs in participating life insurance under mean–variance preferences

Transaction costs with respect to distribution and administration play a crucial role for the performance of participating life insurance products. The aim of this paper is to investigate the impact of such initial and annual transaction costs on policyholder mean–variance preferences depending on the contract features, comparing a point-to-point guarantee, a cliquet-style guarantee, and a money-back guarantee with annual surplus component. We extend previous work by deriving analytical solutions for the maximum allowed initial transaction costs as well as the risk aversion parameter that ensure a given customer preference level for different contract types. We further conduct simulation analyses to identify key factors in regard to transaction costs. One main finding is that in the present setting, insurers can indeed charge higher costs for more complex products with cliquet-style features, and that the difference in costs between the various product types increases considerably in a low interest-rate environment. However, these results are heavily impacted and even reversed depending on the risk–return asset characteristics, as insurers with a riskier asset management strategy may no longer be able to charge higher transaction costs for complex products with a strong annual cliquet-style surplus participation component without reducing their attractiveness to customers.     

Developing the roots of modelling conceptions: ‘mathematical modelling is the life of the world’

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a Modelling conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity, actions and conceptions of both modelling and mathematics that these beginners to modelling displayed. Understanding the conceptions of mathematics that students might hold or be developing and how these can be influenced in early schooling are essential ingredients in any plans for introducing modelling seriously into primary school classrooms. The majority of the students (22/25) were identified as displaying a developing conception of modelling as a way of problem handling. The three other students displayed the developmental roots of a way of understanding the world conception of modelling. These three students also displayed a Modelling conception of mathematics with one showing indications of developing towards a Life conception of mathematics.     

Assessing e-Participation via user’s satisfaction measurement: the case of OurSpace platform

The field of e-Participation is expanding as many similar platforms have been created to elicit citizens’ opinions on political and social issues in modern democracies especially under political and economic crises. The development of the field has been supported by emerging web technologies such as social networking, data mining, sentiment analysis and collaborative systems. This paper presents a methodological framework to assess the main dimensions of an e-Participation system from the users’ perspective by measuring users’ satisfaction and highlighting its advantages and identifying its shortcomings in order to propose areas for improvement. The method refers to an e-Participation platform developed in the scope of the e-Participation project OurSpace. The evaluation framework of the project was realized through a questionnaire, suitably designed to be in line with the Whyte and Macintosh theory of three perspectives: social, technical and political. The assessment of the OurSpace platform was performed through the multi-criteria satisfaction analysis method. The method provided all satisfaction diagrams and indices so as to determine the users’ opinion about OurSpace e-Participation system and point out the needed actions towards improvement.     

On the Geometrical Meaning of the Dynamic Equations in Analytical Mechanics

In this paper,the modern geometrical structure of analytical mechanics,the exteriordifferential forms and the geometrical meaning of dynamic equations are briefly discussed.     

Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement

The purpose of this study was to examine middle school students’ proportional reasoning, solution strategies and difficulties in real life contexts in the domain of geometry and measurement. The underlying reasons of the difficulties were investigated as well. Mixed research design was adopted for the aims of the study by collecting data through an achievement test from 935 sixth, seventh and eighth grade students. The achievement test included real life problems that required proportional reasoning, and were related to the measurement of length, perimeter, area and volume concepts. In addition, task-based interviews were conducted on 12 of these students to collect more comprehensive data and to support the findings of the achievement test. Findings revealed that although students were mostly successful in giving correct answers, their reasoning lacked a clear argument of the direct and indirect proportional relationships between the variables and that they approached the problems by superficial characteristics of the problems.     

Assessing systematic sampling in estimating the Banzhaf–Owen value

This paper addresses a general sampling method to estimate the Banzhaf–Owen value for general cooperative TU-games. It is based on systematic sampling techniques on the set of those coalitions that are compatible with the structure of a priori unions. This procedure is theoretically analysed by establishing a collection of statistical properties. Finally, we evaluate this tool on approximating the power of the members of the Executive Board of Governors of the International Monetary Fund (IMF) in 2002 and 2016.     

Free products of cyclic subgroups in the groupPSL 2(ℂ)

In the paper, families of faithful representations of the free product ofn (n ≥ 2) cyclic groups into the groupPSL ₂(ℂ) are indicated. They are used to generalize a result of Ree and Mendelsohn. We also obtain a series of sufficient conditions under which a 2-generated subgroup 〈A, B〉 of the groupPSL ₂(ℂ) is isomorphic to the free product of its cyclic subgroups 〈A〉 and 〈B〉. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 922–930, June, 2000.     

Pták’s characterization of reflexivity in tensor products

We characterize the reflexivity of the completed projective tensor products of Banach spaces in terms of certain approximative biorthogonal systems.     

Belief reliability: a new metrics for products’ reliability

Traditional reliability metrics are based on probability measures. However, in engineering practices, failure data are often so scarce that traditional metrics cannot be obtained. Furthermore, in many applications, premises of applying these metrics are violated frequently. Thus, this paper will give some new reliability metrics which can evaluate products’ reliability with few failure data. Firstly, the new metrics are defined based on uncertainty theory and then, numerical evaluation methods for them are presented. Furthermore, a numerical algorithm based on the fault tree is developed in order to evaluate systems’ reliability in the context of defined metrics. Finally, the proposed metrics and evaluation methods are illustrated with some case studies.     

Pay inequity effects on back-office employees’ job performances: the case of a large insurance firm

Central European Journal of Operations Research - Using personnel data on back-office employees of an insurance company, we investigate the effect of pay inequity—as measurable and, hence,...     

Generalization of Lundberg’s inequality for the case of stock insurance company

The ruin probability of an insurance company paying dividends according to a barrier strategy with a step barrier function is considered. Upper bounds for the probability of ruin are obtained within the framework of Sparre Andersen and Cramer–Lundberg risk models.     

Students’ Conceptions of Congruency Through the Use of Dynamic Geometry Software

This paper describes students’ interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK￠ model of conceptions, suggests that incorporating technology in mathematics classrooms enabled a measure-preserving conception of congruency with which students’ could shift focus from shapes to properties. Students also interacted with dynamic diagrams in a novel way, which we call the functional mode of interaction with diagrams, relating outputs and inputs that result when dragging a figure. Students’ participation in classroom interactions through discourse and through actions on diagrams provided evidence of learning using tools within dynamic geometry software.     

An hybrid method that improves the accessibility of Steffensen’s method

Steffensen’s method is known for its fast speed of convergence and its difficulty in applying it in Banach spaces. From the analysis of the accessibility of this method, we see that we can improve it by using the simplified secant method for predicting the initial approximation of Steffensen’s method. So, from both methods, we construct an hybrid iterative method which guarantees the convergence of Steffensen’s method from approximations given by the simplified secant method. We also emphasize that the study presented in this work is valid for equations with differentiable operators and non-differentiable operators.     

Dynamic conformance and design quality in a supply chain: an assessment of contracts’ coordinating power

We consider a two-echelon supply chain involving one manufacturer and one supplier who collaborate on improving both design and conformance quality. Design quality is supposed to increase product desirability, and therefore market demand, while conformance quality should reduce the proportion of defective items, and therefore increase the manufacturer’s sales revenue. We investigate how the supply chain parties allocate effort between design and conformance quality under both cooperative and non-cooperative settings in an intertemporal framework. Furthermore, we evaluate wholesale price contracts and revenue-sharing contracts in terms of their performance and coordination power. We show that although a revenue-sharing contract enables the manufacturer to effectively involve the supplier in quality improvement, neither contract type allows for perfect coordination resulting in the quality that can be achieved by a cooperative supply chain. We thus suggest a reward-based extension to the revenue-sharing contract, to ensure system-wide optimal quality performance. Importantly, we find that the supplier would be better off adopting a reward-based revenue sharing contract and refusing a standard revenue-sharing contract, while the opposite would be true for the manufacturer.