On the Lack of Participating Policy Usage by Stock Insurance Companies

Stock insurers can reduce or eliminate agency conflicts between policyholders and stockholders by issuing participating insurance. Despite this benefit, most stock companies don't offer participating contracts. This study explains why. We study an equilibrium with both stock and mutual insurers in which stockholders set premiums to provide a fair expected return on their investment, and with a policyholder who chooses the insurance contract that maximizes her expected utility. We demonstrate that stockholders cannot profitably offer fully participating contracts, but can profitably offer partially participating insurance. However, when the policyholder participation fraction is high, the fair‐return premium is so large that the policyholder always prefers fully participating insurance from the mutual company. Policies with lower levels of policyholder participation are optimal for policyholders with relatively high risk aversion, though such policies are usually prohibited by insurance legislation. Thus, the reason stock insurers rarely issue participating contracts isn't because the potential benefits are small or unimportant. Rather, profitability or regulatory constraints simply prevent stock insurers from exercising those benefits in equilibrium.     

The 1999 Small Employer Retirement Survey

Abstract

In this article we examine to what extent policyholders buying a certain class of participating contracts (in which they are entitled to receive dividends from the insurer) can be described as standard bondholders. Our analysis extends the ideas of Biihlmann and sequences the fundamental advances of Merton, Longstaff and Schwartz, and Briys and de Varenne. In particular, we develop a setup where these participating policies are comparable to hybrid bonds but not to standard risky bonds (as done in most papers dealing with the pricing of participating contracts). In this mixed framework, policyholders are only partly protected against default consequences. Continuous and discrete protections are also studied in an early default Black and Cox-type setting. A comparative analysis of the impact of various protection schemes on ruin probabilities and severities of a life insurance company that sells only this class of contracts concludes this work.     

The market of dynamic hybrid products in Germany: concept, risk-return profiles, and market overview

This article analyzes dynamic hybrid products along with their diverse characteristics and contract variations that are currently available in the German market. Dynamic hybrid products are innovative life insurance contracts combining features of traditional participating life insurance with those of unit-linked policies. This approach is thereby implemented by a mathematical algorithm based on a constant proportion portfolio insurance strategy that periodically reallocates funds (e.g. once per month or day) between the policy reserve stock (with an interest rate guarantee), a guarantee fund and/or equity fund. In this paper, we contribute to the literature by examining the concepts and key features of available dynamic hybrid products with particular focus on the embedded options, which allows the identification of key contract characteristics associated with them. In addition, risk-return profiles are studied and compared, which is of high relevance for regulators and policyholders. Our results show that these strongly vary, depending on the individual rebalancing mechanism and the type and amount of embedded options.     

Understanding Basis Risk in Insurance Contracts

There is a tremendous amount of resources being tied up in litigation between insurance companies and policyholders over things like the extent of coverage for various loss scenarios or allegedly bad faith delays in settlement payments. The fact that policyholders formally dispute insurer coverage positions or claims payment strategies gives credibility to the idea that mismatches exist between what policyholders expect insurance policies to cover and what the insurance contracts actually provide as loss indemnification. This mismatch essentially represents insurance basis risk, the analysis of which can more accurately reflect the value and overall efficiency of insurance contracts and suggest factors that may influence policyholder dissatisfaction and consequently insurance contract disputes. This article takes a detailed look at insurance basis risk and finds that subjectivity plays a prominent role in its definition. Using Bayesian inference, it is shown how factors can affect the magnitude of insurance basis risk depending on the individual situation in which the mismatch between losses and coverage exists.     

Risk assessment of surplus appropriation schemes in participating life insurance

The aim of this paper is to analyze a life insurance company’s risk exposure with respect to different surplus appropriation schemes in participating life insurance. In this regard, three surplus appropriation schemes are considered, including the bonus system, the interest-bearing accumulation, and the system of shortening the contract term. We further examine an insurance company that offers all three schemes, i.e. each system is used for one third of the policyholders. Focus is laid on the effect of different asset portfolios and shocks to mortality on the insurer’s risk situation with respect to the policyholder’s age level at contract inception.     

Commitment and Lapse Behavior in Long‐Term Insurance: A Case Study

This article presents a case study of a portfolio of individual long‐term insurance contracts sold by a Spanish mutual company. We describe the risk levels, the rating structure, and the implied cross‐subsidies on a portfolio of policies providing health, life, and long‐term care insurance. We show evidence of reclassification risk through the history of disability spells. We also analyze the lapse behavior and seek to provide a rationale for the portfolio’s dynamics. We discuss the lack of commitment from the policyholders (lapses) and from the mutual company (which took a run‐off decision). Finally, we draw conclusions regarding the design of such contracts.     

Mortality-Indexed Annuities Managing Longevity Risk Via Product Design

Abstract

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries. In its aggregate form, the systematic risk of changes to general mortality patterns, it has the potential for causing large cumulative losses for insurers. Since obvious risk management tools, such as (re)insurance or hedging, are less suited for managing an annuity provider’s exposure to this risk, we propose a type of life annuity with benefits contingent on actual mortality experience.

Similar adaptations to conventional product design exist with investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience can be found in German private health insurance. By effectively sharing systematic longevity risk with policyholders, insurers may avoid cumulative losses.

Policyholders also gain in comparison with a comparable conventional annuity product: Using a Monte Carlo simulation, we identify a significant upside potential for policyholders while downside risk is limited.     

Insurance guaranty fund—what good is it?

In this paper, we analyze under which conditions a self-supporting insurance guaranty fund can be beneficial for the policyholders in an incomplete market. Within the analyzed setting, we find out that in general, if existent, the potential advantages from its introduction cannot be fairly divided among the participating insurers. Thereby, we have to expect systematic wealth transfers between the policyholders of different insurance companies. We introduce a framework for utility-based fund charges as a solution to this problem.     

Consumer risk perceptions and information in insurance markets with adverse selection

Standard models of adverse selection in insurance markets assume policyholders know their loss distributions. This study examines the nature of equilibrium and the equilibrium value of information in competitive insurance markets where consumers lack complete information regarding their loss probabilities. We show that additional private information is privately and socially valuable. When the equilibrium policies separate types, policyholders can deduce the underlying probabilities from the contracts, so it is information on risk type, rather than loss probability per se, that is valuable. We show that the equilibrium is “as if” policyholders were endowed with complete knowledge if, and only if, information is noiseless and costless. If information is noisy, the equilibrium depends on policyholders' prior beliefs and the amount of noise in the information they acquire.     

Modeling the Impact of Genetics on Insurance

The role of probabilistic models in the debate over genetics and insurance is discussed. A Markov model is used to show that, under quite extreme assumptions, adverse selection in life insurance ought to be controllable. The statistical problems of estimating small differences in mortality are discussed; these might limit the use of many genetic disorders as rating factors. The influence of the insurance industry on policy-making, especially through its support of research, is discussed. It is suggested that participating contracts are suitable and simple vehicles to carry the genetic risks in life insurance.     

Zur bedeutung einer Ausfallbedrohtheit von Versicherungskontrakten — ein Beitrag zur Behavioral Insurance

Kahneman / Tversky 1979 introduced the notion of so-called probabilistic insurance contracts. These are insurance policies involving a small probability that the consumer is not reimbursed because of a possible default of the insurance company. Extending the study ofWakker / Thaler / Tversky 1997, the present study contains an experimental analysis of the willingness of potential policyholders to pay for probabilistic insurance in dependency on the rating of the insurance company. It can be shown that people dislike probabilistic insurance and demand a substantial reduction in the premium to compensate for default risk. This reduction is rising with the default risk of the company. In addition, the results show a new phenomenon. The more an insurance company is threatened by default risk the less people are willing to accept contracts of this company at all. Finally the paper discusses implications for the control of insurance companies.     

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.     

Insurance Markets With Differential Information

This article attempts to understand the outcomes when each party of an insurance contract simultaneously has superior information. I assume that policyholders have superior information about specific risks while insurers have superior information about general risks. I find that low-general-risk policyholders purchase insurance, while high-general-risk policyholders are self-insured. Among the low-general-risk policyholders, high-specific-risk policyholders purchase full insurance, while low-specific-risk policyholders purchase partial insurance. When insurers can strategically publicize their information, efficiency is improved because high-general-risk policyholders purchase actuarially fair insurance. The market segmentation is also found based on the general-risk type and the publicizing of information.     

Implicit Options in Life Insurance: Valuation and Risk Management

Participating life insurance contracts typically contain various types of implicit options. These implicit options can be very valuable and can thus represent a significant risk to insurance companies if they practice insufficient risk management. Options become especially risky through interaction with other options included in the contracts, which makes their evaluation even more complex. This article provides a comprehensive overview and classification of implicit options in participating life insurance contracts and discusses the relevant literature. It points out the potential problems particularly associated with the valuation of rights to early exercise due to policyholder exercise behavior. The risk potential of the interaction of implicit options is illustrated with numerical examples by means of a life insurance contract that includes common implicit options, i.e., a guaranteed interest rate, stochastic annual surplus participation, and paid-up and resumption options. Valuation is conducted using risk-neutral valuation, a concept that implicitly assumes the implementation of risk management measures such as hedging strategies.     

The Effect of Risk Aversion and Loss Aversion on Equity-Linked Life Insurance With Surrender Guarantees

We price equity-linked life insurance with surrender guarantees and account for risk preferences in the form of risk-averse and loss-averse policyholders in continuous time. Risk-averse policyholders surrender their policy for higher equity index values. Compared to optimally surrendered policies, this behavior creates substantial policy value losses. In contrast, loss-averse policyholders surrender once the surrender benefit realizes a gain but keep under-performing policies. This disposition effect reduces the policy value relative to both optimally surrendered policies and policies surrendered by risk-averse policyholders. Insurers in competitive markets need to estimate their policyholders’ risk preferences accurately.     

Market Consistent Embedded Value in der privaten Krankenversicherung

The Market Consistent Embedded Value (MCEV) allows for a principal based valuation of insurance contract portfolios. An important aspect of the MCEV methodology is the possibility to compare different insurance companies. In this paper we introduce the valuation principles with respect to German private health insurance. To this end we first explain the different components of a MCEV. In the following we discuss the relevant aspects of market consistent valuation of German private health insurance and show, how financial options and guarantees of private health insurance contracts influence the shareholder value. In particular we analyze the impact of surplus distribution and the different surrender options of policyholders on the value.     

Don’t lapse into temptation: a behavioral explanation for policy surrender

Many policyholders surrender their life insurance policies early, leading to substantial monetary losses for private households. Surrender can be explained rationally if it constitutes the last resort providing liquidity in the event of an urgent need of cash. Yet we find clear evidence in German panel data that for more than half of all surrendered contracts investors had cheaper options available to provide the required liquidity. This finding demonstrates that there must be other factors influencing this important life decision. We provide a behavioral explanation, focusing on the role of individual decision heuristics, financial literacy, and financial advice. In particular, we show that financial literacy and financial advice can mitigate the behavioral temptation to lapse, while the tendency to rely on heuristics increases lapse probability.     

Vertragsrechtliche Anforderungen an die Gestaltung von „Self-Tracking“-Tarifen in der Privatversicherung

The phenomenon of digitalization is reaching into our everyday lives, and “self-tracking” practices gain new adherents. Yet “self-tracking”, the practice of systematically recording information about one’s health and lifestyle by digital means, is not only an opportunity for the self-tracker to enhance his self-knowledge, but also for insurers to detail and personalize their risk assessment. The following article deals with “self-tracking”-insurance contracts, i.?e. insurance contracts that adapt to the personal risk data of the insured person and offer discounts for risk-aware policyholders. In these contracts, self-tracking data will either be used as a basis for premium calculation or as an element to calculate the bonuses payable as profit participation on with-profit policies. The article focuses on the control of standard terms of “self-tracking”-insurance contracts, but also covers the legal prerequisites under which the insurance contract may be combined with a separate self-tracking-contract between the self-tracker and a third party.     

中国分红保险的机理与制度框架

分红政策在分红保险的经营和监管中始终发挥着核心作用。不论分红保险采用何种模式,分红政策都应当遵循一定的原则:既重视保单持有人的合理预期,贯彻诚信经营和红利分配的公平原则,又要充分考虑红利分配对公司未来红利水平、投资策略以及偿付能力的影响。为了实现分红保险的这些原则,必须辅以有效的工具,其中分红特别储备是实现这些目的的本质、核心和关键。本文以此为基础,阐述了分红保险的管理机制和报告制度。