Individual Policyholder Research Articles

Building resilience in cybersecurity: An artificial lab approach

AbstractBased on classical contagion models we introduce an artificial cyber lab: the digital twin of a complex cyber system in which possible cyber resilience measures may be implemented and tested. Using the lab, in numerical case studies, we identify two classes of measures to control systemic cyber risks: security‐ and topology‐based interventions. We discuss the implications of our findings on selected real‐world cybersecurity measures currently applied in the insurance and regulation practice or under discussion for future cyber risk control. To this end, we provide a brief overview of the current cybersecurity regulation and emphasize the role of insurance companies as private regulators. Moreover, from an insurance point of view, we provide first attempts to design systemic cyber risk obligations and to measure the systemic risk contribution of individual policyholders.

Cognitive ability impact on life insurance lapsation


 
 
 Life insurance is an important household risk management and financial tool. Policy lapsation has economic effects on life insurance companies, policyholders, and beneficiaries that may be detrimental when these lapses are unexpected. Prior literature examined several hypotheses of life insurance lapse focusing mainly on macroeconomic factors using aggregate data and household microeconomic factors using household-level data. We introduce and test individual cognitive ability variables in a model of the life insurance voluntary lapse decision by individual policyholders using household-level data from the Health and Retirement Study. We find that one measure of cognitive ability, in particular, numer- acy, is related to the voluntary lapse decision. While controlling for numeracy, we find evidence that those individuals with higher levels of net worth are less likely to voluntarily lapse a policy which is consistent with the emergency fund hypothesis. We introduce a new measure of liquidity shock, kids moving home, into the model and find it has a strong positive relationship with the decision to voluntar- ily lapse a policy. Consistent with life insurance demand theory, we find that those who have recently entered retirement are more likely to lapse their policy.
 
 

Ratemaking in a changing environment

AbstractIn pricing insurance contracts based on the individual policyholder’s aggregate losses for non-life insurers, the literature has mainly focused on using detailed information from policies and closed claims. However, the information on open claims can reflect shifts in the distribution of the expected claim payments better than closed claims. Such shifts may be needed to be reflected in the ratemaking process earlier rather than later, especially when insurers are experiencing environmental changes. In practice, actuaries use ad hoc techniques to adjust data to current levels to determine premiums. This paper presents an intuitive ratemaking model, employing a marked Poisson process framework, which ensures that the multivariate risk analysis is done more routinely using all reported claims and makes an adjustment for Incurred But Not Reported claims. Utilizing data from the Wisconsin Local Government Property Insurance Fund, we find that by determining rates based on current data, the proposed ratemaking model leads to better alignment of premiums and provides insurers with a more financially sound portfolio.

Driving risk prevention in usage-based insurance services based on interpretable machine learning and telematics data

Usage-based insurance (UBI) adjusts premiums based on an individual policyholder’s dynamic risk evaluation, incentivizing policyholders to maintain safe driving behavior in pursuit of a lower insurance premium. Although post-trip interventions can improve driving behavior significantly, most interventions do not provide risk mitigation strategies tailored to long-term driving behavior. This study proposes a novel approach for driving risk prevention in UBI services, providing risk analysis services and tailoring driving suggestions for policyholders. Advanced prediction models and model interpretation methods were adopted to assess and analyze personal driving risks, respectively. A multi-objective counterfactual model was developed to generate risk mitigation strategies for policyholders. The significance of driving behavior in risk mitigation and its actionability were assessed to provide realistic and actionable suggestions for policyholders. The case study, based on a real dataset from an insurance company in China, showed that the proposed approach can be directly embedded in the existing UBI service framework to provide personalized feedback and services to policyholders.

Multivariate Insurance Portfolio Risk Retention Using the Method of Multipliers

For an insurance company insuring multiple risks, capital allocation is an important practical problem. In the capital allocation problem, the insurance company must determine the amount of capital to assign to each policy or, equivalently, the amount of premium to be collected from each policy. Doing this relates to the problem of determining the risk retention parameters for each policy within the portfolio. In this article, the insurance risk retention problem of determining the optimal retention parameters is explored in a multivariate context. Given an underlying claims distribution and premium constraint, we are interested in finding the optimal amount of risk to retain or, equivalently, which level of risk retention parameters should be chosen by an insurance company. The risk retention parameter may be deductible (d), upper limit (u), or coinsurance (c). We present a numerical approach to solving the risk retention problem using the method of multipliers and illustrate how it can be implemented. In a case study, the minimum amount of premium to be collected is used as a constraint to the optimization and the upper limit is optimized for each policyholder. A Bayesian approach is taken for estimation of the parameters in a simple model involving regional effects and individual policyholder effects for the Wisconsin Local Government Property Insurance Fund (LGPIF) data, where the parameter estimation is performed in the R computing environment using the Stan library.

Surrender contagion in life insurance

Modern life insurance policies embed a surrender option that entitles policyholders to terminate their policy early for its cash value. Mass surrenders–spiking surrenders of life insurance policies within a short period–are widely documented prior to many life insurer failures, but their impacts on insurers are rarely quantified. This paper builds a model of mass surrenders in a heterogeneous pool consisting of a minority of financially guided policyholders who make rational surrender decisions and a majority of individual policyholders who are subject to herd. By revising the self-excitation in the Hawkes process to a contingent event-accumulation-excitation, we introduce a history-dependent surrender process for the individuals whose contagious behavior can be triggered contingent on past surrenders becoming salient. We then incorporate it into a life insurance pricing framework and study mass surrenders’ impacts on contract valuation and default risk of the insurer, allowing for its structural default under regulatory solvency intervention. Our numerical results show that while contagion aligns individual policyholders’ surrender behavior with the optimal surrender of financially guided ones, it jeopardizes their financial positions in favor of equity holders. Surprisingly, surrender contagion only mildly enlarges an insurer’s bankruptcy rate, which is not driven by strict solvency regulation. Despite its public perception of posing a significant risk to insurers as similar to a bank run, surrender contagion does not critically threaten insurers’ solvency: To prevent insurers’ bankruptcies, their investment riskiness and leverage pose more of a concern to regulators.

Telematics Insurance: Legal Concerns and Challenges in the EU Insurance Market

This paper assess the legal challenges arising from the use of telematics technology in the insurance sector. Telematics technology allows insurers to obtain information on location, kilometres travelled and other driving patterns of an individual policyholder. Ultimately, this will allow car insurers to use risk factors related to an individual policyholder to determine the premium for motor vehicle liability insurance. For all its possible benefits, telematics insurance poses significant privacy and data protection risks, revolving around two questions: first, whether insurers can collect certain data on driver’s habits and behaviour; second, how this data is used (and processed) by the insurers. The paper will rely on a legal analysis of the legislative texts on which data protection and privacy are based in Europe and will be supported by a review of the relevant academic literature, research reports and other policy documents, industry publications and media materials. Part One will introduce telematics insurance focusing on the insurance sector in the European Union. Part Two addresses in more detail the main legal challenges posed by telematics insurance, data protection and privacy. Part Three points out other challenges facing telematics insurance, including data ownership and indirect discrimination. In conclusion, this paper looks ahead to possible insurance sector responses and policy goals.

DISCRIMINATION-FREE INSURANCE PRICING

AbstractWe consider the following question: given information on individual policyholder characteristics, how can we ensure that insurance prices do not discriminate with respect to protected characteristics, such as gender? We address the issues of direct and indirect discrimination, the latter resulting from implicit learning of protected characteristics from nonprotected ones. We provide rigorous mathematical definitions for direct and indirect discrimination, and we introduce a simple formula for discrimination-free pricing, that avoids both direct and indirect discrimination. Our formula works in any statistical model. We demonstrate its application on a health insurance example, using a state-of-the-art generalized linear model and a neural network regression model. An important conclusion is that discrimination-free pricing in general requires collection of policyholders’ discriminatory characteristics, posing potential challenges in relation to policyholder’s privacy concerns.

Niepewność interpretacyjna zapisów ochrony ubezpieczeniowej konsumentów ubezpieczeń na życie oferowanych do kredytów mieszkaniowych na przykładzie wybranych ofert

Bundled package of home loans and insurance are a natural phenomenon. Banks treat insurance as the primary security for the credit. For the consumer–borrower can help in financial difficulty. The purpose of insurance added to the loan is to reduce the risk of inability of borrowers to pay back their loans to banks and to ensure the safety of the insured or beneficiary of the insurance policy Therefore, insurance added to the loans should effectively protect borrowers. However, bundled package entails the risk of mismatching the insurance cover with the individual policy-holder insurance needs. Consumer–borrower may not be aware of the scope of insurance protection, which results from the insurance contract and general insurance terms and conditions. Therefore, in order to properly understand the offer of insurance, it becomes necessary to familiarize the borrower–the consumer with the general insurance conditions. However, as research shows, there is a big problem on the insurance sector with unintelligible insurance policy.
 The purpose of the article/hypothesis: The aim of the article is to compare and assess the scope of insurance cover based on the provisions of the general conditions of life insurance added to home loans by the two largest banks in Poland.
 Methodology: The article uses a comparative analysis of the scope of insurance cover on the based on provisions of the general conditions of insurance. The following categories have been selected from the general conditions of insurance: subject of insurance, definitions of events covered by the liability of the insurer, nature of benefits, amount of insurance and exclusions and limitations of liability.
 Results of the research: the analysis of the scope of insurance cover at selected banks in the article shows that selected categories from the general terms and conditions of insurance limit the potential level of insurance cover. After reviewing the general terms and conditions of insurance, consumer–borrower is not sure whether he will get help from the insurer when he needs it.

The representative heuristic and catastrophe-related risk behaviors

Building on the work by Volkman-Wise Journal of Risk and Uncertainty, 51, 267–290 (2015) and Dumm et al. (The Geneva Risk and Insurance Review, 42, 117–139 (2017), we examine behavioral aspects of risk through the representative heuristic’s impact on catastrophe-related probability assessment and insurance demand of Florida homeowners. The representative heuristic models individuals as underweighting prior probabilities and overweighting posterior probabilities, thereby overweighting the probability of a loss from a disaster after a disaster occurs. Using data for homeowners’ insurance purchases through Florida’s residual market over a time period (2003-2008) that includes a sub-period of many losses (2004-2005) and sub-period of few catastrophic losses (2003, 2006-2008), we find increases in demand at the individual policyholder level for coverage following losses. Also consistent with the representative heuristic, we find that the effect attenuates as the losses fade from memory. That is, the effect of losses on demand is much higher for more recent losses. We also are able to parameterize the representative heuristic model showing that individual policy holders overweight the probability of another catastrophic event occurring by nearly 50%, after one has occurred.

Discrimination-Free Insurance Pricing

A simple formula for non-discriminatory insurance pricing is introduced. This formula is based on the assumption that certain individual (discriminatory) policyholder information is not allowed to be used for insurance pricing. The suggested procedure can be summarized as follows: First, we construct a price that is based on all available information, including discriminatory information. Thereafter, we average out the effect of discriminatory information. This averaging out is done such that discriminatory information can also not be inferred from the remaining non-discriminatory one, thus, neither allowing for direct nor for indirect discrimination.

Surrender Contagion in Life Insurance: Modeling and Valuation

Mass surrenders—spiking surrenders of life insurance policies within a short period— are widely documented prior to many life insurers failures, but their impacts on insurers are rarely quantified. This paper builds a model of mass surrenders in a heterogeneous pool consisting of a minority of financially guided policyholders and a majority of individual policyholders with contagious behavior that can be triggered contingent on past surrenders becoming salient. By incorporating it into a life insurance pricing framework, we study mass surrenders’ impacts on contract valuation and early bankruptcy of the insurer, allowing for its structural default under regulatory solvency intervention. Our numerical results show that while contagion aligns individual policyholders’ surrender behavior with the optimal surrender of financially guided ones, it jeopardizes their financial positions in favor of equity holders. Surprisingly, contagion at worst only marginally enlarges the insurer’s bankruptcy rate, which is not driven by strict solvency regulation. Insurers have incentives to encourage contagion. Despite its public perception of endangering market stability as similar to a bank run, surrender contagion does not threaten insurers’ solvency, but can improve it instead with the assets left behind by individual policyholders.

Graphic and Numerical Evolution of a Bonus-Malus System via Markov Chain Models

Abstract This paper describes an online solution for visualizing the simulation of a discrete time Markov chain using an animated graph. Based on the D3.js library, the development of this solution offers the user the choice between a presentation based on the concept of a probabilistic graph oriented and a presentation of the transitions in a matrix framework. As an application the solution helps to describe the dynamics of individual policyholders in a Bonus-Malus system of automobile insurance.

Optimal Insurance Strategy in the Individual Risk Model under a Stochastic Constraint on the Value of the Final Capital

We solve a problem of optimal risk control in the static model by choosing an admissible insurance policy, where the objective functional is the so-called Markowitz utility functional, i.e., a functional that depends only on the mean value and standard deviation of the insurer’s final capital after an insurance transaction. Interests of the insurer are taken into account by introducing probabilistic or, more precisely, quantile constraints (value at risk constraint) on the final capital of the insurer, using a normal distribution to model the distribution of total damage. Additionally, we impose a restriction with probability one on the risk taken from an individual policy holder. Optimal from the point of view of the insurer is the so-called stop-loss insurance. We find explicit forms of conditions for refusing an insurance transaction. We give an example that illustrates the proven results in case of an exponential distribution of claim size.

The impact of internal forces on acceptance of takaful by insurance policy-holders in India

PurposeInsurance is a modern risk-management tool. Although the idea is novel, its practice is not free of interest, uncertainty and elements of gambling. Takaful has been introduced as an alternative to modern insurance. India has an established insurance industry, and although the country has the second largest Muslim population in the world, takaful has not been introduced there. Moreover, no research has examined how internal forces affect policy-holders to buy new insurance products such as takaful in India. This study aims to examine whether internal factors influence individual insurance policy-holders to open up to takaful. As internal factors reflect the innovative nature of policy-holders, this paper seeks to determine whether there is significant difference in the innovative nature of two independent sample groups (e.g. between Muslims and non-Muslims) in participating in takaful.Design/methodology/approachNew product adoption theory is used in developing the hypotheses and a questionnaire. Snowball sampling method is used in this survey, with a sample size of 909 respondents, including Muslim and non-Muslim policy-holders. The internal forces that encourage potential policy-holders to participate in takaful is the independent variable here, while the respondents’ actual willingness to participate in takaful is the dependent variable. Religion and level of education are used as control variables, and regression and T-tests are performed to analyze the data.FindingsResults show that the internal factors have significant impact at 1 per cent on the acceptance of takaful by policy-holders. There is also a significant difference in the innovative nature between Muslims and non-Muslims. Mean values from the T-test show that Muslims are more innovative than non-Muslims in India, offering a good sign for India to start offering takaful, as Muslims could be the core customer base.Research limitations/implicationsThis study focuses on internal factors influencing individual policy-holders’ willingness to participate in takaful. The findings can be the starting point for future research exploring the influence of external factors on such willingness to participate with potential benefits to local authorities, investors, insurance companies and the public in India.Originality/valueThis study provides crucial information about the demand side of takaful in India. The innovative nature of Indian policy-holders signals positive potential for operators to offer takaful in India and to concerned regulatory bodies to expedite its introduction to the market.

MEASURING THE IMPACT OF A BONUS-MALUS SYSTEM IN FINITE AND CONTINUOUS TIME RUIN PROBABILITIES FOR LARGE PORTFOLIOS IN MOTOR INSURANCE

AbstractMotor insurance is a very competitive business where insurers operate with quite large portfolios, often decisions must be taken under short horizons and therefore ruin probabilities should be calculated in finite time. The probability of ruin, in continuous and finite time, is numerically evaluated under the classical Cramér–Lundberg risk process framework for a large motor insurance portfolio, where we allow for a posteriori premium adjustments, according to the claim record of each individual policyholder. Focusing on the classical model for bonus-malus systems, we propose that the probability of ruin can be interpreted as a measure to decide between different bonus-malus scales or even between different bonus-malus rules. In our work, the required initial surplus can also be evaluated. We consider an application of a bonus-malus system for motor insurance to study the impact of experience rating in ruin probabilities. For that, we used a real commercial scale of an insurer operating in the Portuguese market, and we also work on various well-known optimal bonus-malus scales estimated with real data from that insurer. Results involving these scales are discussed.

Adjusting the Premium Relativities in a Bonus-Malus System: An Integrated Approach Using the First Claim Time and the Number of Claims

Abstract In this paper, we propose an integrated approach to adjust the premium relativities in a bonus-malus system by using the information of the first claim time (expressed in terms of sub-period in a year) and the number of claims reported by individual policyholder. We provide a formal representation for the newly proposed structure and derive the analytical expressions for the adjusted premium relativities. Other things being equal, a lower adjusted premium relativity is imposed for an earlier sub-period of the first claim made, whereas policyholders with more claims are subject to a higher adjusted premium relativity.

Modelling a BMS-based automobile liability rating system: The Serbian case

In this paper the authors examine the viability of applying a bonusmalus system in establishing automobile liability premium rates. They have developed an optimal tariff system which reflects the equivalence principle between the amounts of the premiums and the reported losses of individual policyholders. Based on past incidents of the policyholders, a homogeneous distribution of the risk classes and an improved insurance rating have been obtained. The developed model was tested with the negative binomial distribution and the expected value principle on a sample of 98,978 policyholders in Serbia. As a result, the set tariff system has been financially balanced, i.e. a balance was struck between the cost amounts of total premiums among policyholders and the cost amount of expected future claims. It has been proven that, in the process of modelling the automobile liability rating system based on the frequency of claims, it is optimal to use sophisticated distribution models such as the negative binomial distribution.

Application of a Discrete-time Markov Chain Simulation in Insurance

This paper describes the application of an online interactive simulator of discrete-time Markov chains to an automobile insurance model. Based on the D3.js library, an interactive visual animation depicts the dynamics of individual policyholders in a bonus-malus system of automobile insurance. A survey was conducted among MSc students who used the simulator to obtain a preliminary assessment of the perceived usefulness in several dimensions of their learning process. The main findings indicate that flexible access via different devices was the most valued feature of this resource. In addition, the possibility of experimenting and simulating by means of controlling the main parameter of the model was also found to be particularly useful.

Integral and differential equations for the moments of multistate models in health insurance

The moments of the random future liabilities of health insurance policies are key quantities for studying distributional properties of the future liabilities. Assuming that the randomness of the future health status of individual policyholders can be described by a semi-Markovian multistate model, integral and differential equations are derived for moments of any order and for the moment generating function. Different representations are derived and discussed with a view to numerical solution methods.