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.     

Equilibrium in Competitive Insurance Markets Under Adverse Selection and Yaari's Dual Theory of Risk

Under Yaari's dual theory of risk, we determine the equilibrium separating contracts for high and low risks in a competitive insurance market, in which risks are defined only by their expected losses, that is, a high risk is a risk that has a greater expected loss than a low risk. Also, we determine the pooling equilibrium contract when insurers are assumed non-myopic. Expected utility theory generally predicts that optimal insurance indemnity payments are nonlinear functions of the underlying loss due to the nonlinearity of agents' utility functions. Under Yaari's dual theory, we show that under mild technical conditions the indemnity payment is a piecewise linear function of the loss, a common property of insurance coverages.     

On the design of optimal health insurance contracts under ex post moral hazard

We analyze the design of optimal medical insurance under ex post moral hazard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-off between ex ante risk sharing and ex post incentive compatibility is analyzed in an optimal revelation mechanism under hidden information and risk aversion. The optimal contract provides partial insurance at the margin, with a deductible when insurers’ rates are affected by a positive loading, and it may also include an upper limit on coverage. The potential to audit the health state leads to an upper limit on out-of-pocket expenses.     

中国的“影子保险”:来自监管自然实验的证据

影子保险在金融稳定中扮演着重要角色,但现有文献较多关注影子银行,对影子保险关注不足。“影子保险”即保险公司通过再保险方式将保险业务转移给不受监管或者受监管较弱的关联企业的活动,这会推高其真实的杠杆水平,增加金融体系脆弱性。然而,由于影子保险的不透明性和缺少自然实验,现有研究仅基于有限数据或模型给出简单的特征事实或结构性估计,很少能从因果关系上清楚地识别影子保险活动及其机制。本文利用中国加强对中资保险公司(处理组)再保险关联交易监管的政策冲击这一自然实验,使用微观数据和双重差分方法,识别了中国金融体系中的影子保险活动。研究发现,相关监管有效降低了影子保险活动,这一效应对集团公司的影响尤为显著;在机制方面,相关监管通过影响中资保险公司资产负债表两端的结构性调整进而降低了其风险承担行为,提高了经营稳定性。本文方法对识别金融机构的监管套利和防范系统性金融风险具有一定参考意义。     

Contingent Commissions and the Management of the Independent Agency

Insurance agencies continue to exist as an important distribution mechanism because they give their contracting insurers advantages in risk selection and enable insurance applicants to transfer complex risks. While independent agencies are compensated by upfront commissions, a key component of their profitability is tied to contingent commissions. A contingency arrangement represents ex post compensation normally tied to underwriting profitability, volume, and annual growth. We report two actual contingency contracts in the context of a decision process for choosing among contingency offerings by insurers. We incorporate both uncertainty and correlation among key variables to arrive at values for competing contracts, then use a downside risk approach that helps agency owners select the better contract. The approach offered in this article is scalable to a selection problem for any number of contingency arrangements.     

A Theory of the Demand for Underwriting

We examine the demand for underwriting and its effect on equilibrium in an insurance market in which insureds know their risk type, but insurers do not. Our analysis indicates that a set of policies including one that requires buyers to take an underwriting test can constitute a full coverage Nash equilibrium when perfect classification is possible. We also find that underwriting equilibria, in which low risks obtain greater coverage than they would without underwriting, widely exist in a Wilsonian market with nonmyopic insurers. Our findings provide a potential explanation for why empirical evidence on adverse selection is mixed.     

论投保人缴纳保费或保险公司签发保单附条件条款的法律效力

我国保险实践中普遍将投保人缴纳保费或者保险公司签发保单作为保险合同的成立、生效或者保险责任开始的条件。但该条件不是新《保险法》规定的附条件保险合同所指的条件。同时该附条件条款赋予了保险公司对要约进行承诺时或者履行合同义务时不受时间限制的权利,该附条件条款因不具有合理性应为无效合同条款。     

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.     

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.     

CDS as insurance: Leaky lifeboats in stormy seas

What market features of financial risk transfer exacerbate counterparty risk? To analyze this, we formulate a model which elucidates important differences between financial risk transfer and traditional insurance, using the example of Credit Default Swaps (CDS). We allow for (heterogeneous) insurer insolvency, which captures the possibility that relatively risky counterparties may exist in the market. Further, we find that stable insurers become less stable as the price of the contract decreases. The analysis includes insured parties that have heterogeneous motivations for purchasing CDS. For example, some may own the underlying asset and purchase CDS for risk management, while others buy these contracts purely for trading purposes. We show that traders will choose to contract with less stable insurers, resulting in higher counterparty risk in this market relative to that of traditional insurance; however, a regulatory policy that removes traders can, perversely, cause stable counterparties to become less stable. We conclude with two extensions of the model that consider a Central Counterparty (CCP) arrangement and the consequences of asymmetric information over insurer type.     

The Risk Balls Game: Transforming Risk and Insurance Into Tangible Concepts

The Risk Balls game is used as a game in an introductory insurance course to demonstrate in a tangible way the notion of risk and its relationship to insurance. Through playing with the ``risk balls,' each one representing a different type of risk, the students experience feelings of anxiety about risk, and later, the sense of anxiety reduction when they transfer the risk balls to insurers. The game incorporates complex concepts of risk transfer and risk reduction via pooling and sharing of risk. The mathematical implications of the law of large numbers are physically felt in the classroom when the students experience the relief associated with transferring the risk balls to insurers. The discussion that ensues during the game includes aspects of the underwriting process; moral hazard; adverse selection; the role of agents, insurers, and regulators; and the nature of the insurance contract. The game of risk balls stimulates lively group discussions and provides hands-on experience with risks such as premature death risk or fire risk and the fears associated with them.     

Systemic risk and diversification across European banks and insurers

The mutual and cross company exposures to fat-tail distributed risks determine the potential impact of a financial crisis on banks and insurers. We examine the systemic interdependencies within and across the European banking and insurance sectors during times of stress by means of extreme value analysis. While insurers exhibit a slightly higher interdependency in comparison with banks, the interdependency across the two sectors turns out to be considerably lower. This suggests that downside risk can be lowered through financial conglomeration.     

Cream Skimming: Innovations in Insurance Risk Classification and Adverse Selection

We demonstrate how innovations in insurance risk classification can lead to adverse selection, or cream skimming, against insurers that are slow to adopt such pricing innovations. Using a model in which insurers with insufficient pricing data cannot differentiate between low‐ and high‐risk policyholders and therefore charge both the same premium, we show how innovative insurers develop new risk classification data to identify overcharged low‐risk policyholders and attract them from rival insurers with reduced prices. Less innovative insurers thus insure a growing percentage of high‐risk customers, resulting in adverse selection attributable to their informational disadvantage. Next, we examine two cases in which “Big Data” innovations in risk classification led to concerns about cream skimming among U.S. auto insurers. First, we track the rapid adoption of credit‐based insurance scores as pricing variables in personal auto insurance markets. Second, we examine the growing popularity of usage‐based insurance programs like telematics, plans in which insurers use data on policyholders’ actual driving behavior to set prices that attract low‐risk customers. Issues associated with the execution of such pricing strategies are discussed. In both cases, we document how rival insurers quickly adopt successful innovations to reduce their exposure to adverse selection.     

On the exposure of insurance companies to sovereign risk—Portfolio investments and market forces

A sovereign debt crisis can have significant knock-on effects in the financial markets and put financial stability at risk. This paper focuses on the transmission of sovereign risk to insurance companies as some of the largest institutional investors in the sovereign bond market. We use a firm level panel dataset that covers large insurance companies, banks and non-financial firms from nine countries over the time period from 1 January 2008–1 May 2013. We find significant and robust transmission effects from sovereign risk to domestic insurers. The impact on insurers is not significantly different from that on banks but larger than for non-financial firms. We find that systemically important insurers are more closely linked to the domestic sovereign. Based on European data, we show that risks in sovereign bond portfolios are an important driver of insurer risk, which is not reflected in current insurance regulation (incl. Solvency II in Europe).     

对外开放背景下的外资保险公司监管

外资保险公司的引进所带来的机遇与挑战并存。不应只看到利用外资带来的正面影响,同时还应该正视利用外资给中国保险业带来的潜在风险。只有正确地识别、测量和控制风险,才能真正做到外资保险为我所用。监管机构需要增强对外资保险的监管能力以切实提高监管效果,应建立适应全球金融发展趋势的监管组织体系;转变监管职能和重点;改进监管手段和方式。     

Relative Hedging of Systematic Mortality Risk

A number of problematic issues have arisen in anticipation of the potential role of molecular tests for genetic predispositions to illness in risk assessment by insurance underwriters. We argue in this paper that the regrettable history and current risks of genetic discrimination warrant a presumption that genetic predisposition status should not be used in any nonmedical contexts, unless compelling evidence can demonstrate that serious harm will result to third-party interests without such use. We argue that insurers should not be able to initiate testing for genetic predisposition. We also argue that there are many reasons to doubt whether patients’ test results will result in such serious adverse selection as to cause substantial harm to insurance markets, except possibly at higher policy amounts in life or disability income insurance. We conclude that the burden of proof must be on insurers to demonstrate necessity of use in specific cases in which test availability shows high probability of imminent, serious harm to insurance markets.     

Complete Versus Incomplete Insurance Contracts under Adverse Selection with Multiple Risks

This article extends the standard adverse-selection model for competitive insurance markets, which assumes a single source of risk, to the case where individuals are subject to multiple risks. We compare the following market situations—the case where insurers can offer comprehensive policies against all sources or risks (complete contracts) and the case where different risks are covered by separate policies (incomplete contracts). In the latter case, we consider whether the insurer of a particular risk has perfect information regarding an individual's coverage against other sources of risks. The analysis emphasizes the informational role of bundling in multidimensional screening. When the market situation allows bundling, it is shown that in equilibrium the low-risk type with respect to a particular source of risk does not necessarily obtain partial coverage against that particular risk.     

Risk Taking and Performance of Public Insurers: An International Comparison

We investigate how investor protection, government quality, and contract enforcement affect risk taking and performance of insurance companies from around the world. We find that better investor protection results in less risk taking, as do higher quality government and greater contract enforceability. However, we find only limited evidence that these factors influence firm performance. We conclude that better overall operating environments result in less risk taking by insurers without the concomitant decline in performance. These results imply that better investor protection environments benefit policyholders and outside stockholders by preventing corporate insiders from expropriating wealth from policyholders and outside stockholders.     

Engineered nanomaterials: risk perception,regulation and insurance

Concerns surrounding the health risk of engineered nanomaterials, effective regulation and the lack of specifically tailored insurance products for the nanotechnology sector are putting the industry’s long-term economic viability at risk. From the perspective of the underwriter, this article speculates on the relationship between risk perception, regulation and insurability. In the nanotechnology sector, regulators are currently failing to keep pace with innovation, and insurers generally lack guiding principles for underwriting occupational risk from nanomaterial exposure. Such vulnerabilities when combined with misguided risk perceptions can lead to the overpricing of risk transfer and ill-conceived regulatory initiatives, thus potentially exhausting resources and stifling innovation in the sector. In the absence of well-developed regulatory protocols, the insurance industry has, and will continue, to occupy a key role as an effective lobby in terms of improved risk management practice. We suggest that the insurance industry will increasingly rely on control banding frameworks and ‘risk mitigation at source’ methods developed in conjunction with their clients to manage severe acute diversifiable risks. Long tail risk will continue to represent a serious challenge to insurers and regulators. In the meantime, insurers will have to bridge their current needs with improvised solutions. As an example of one possible solution, we outline a framework that utilizes financial instruments to hedge an insurer’s exposure to uncertain estimates of these long-term risks.     

Time Deductibles as Screening Devices: Competitive Markets

Seminal papers on asymmetric information in competitive insurance markets, analyzing the monetary deductible as a screening device, show that any existing equilibrium is of a separating type. High risks buy complete insurance, whereas low risks buy partial insurance—and this result holds for the Nash behavior as well as for the Wilson foresight. In this article, we analyze the strength of screening based on limitations to the period of coverage of the contract. We show that in this case (1) the Nash equilibrium may entail low risks not purchasing any insurance at all, and (2) under the Wilson foresight, a pooling equilibrium may exist.