Optimal insurance contract under a value-at-risk constraint

This study develops an optimal insurance contract endogenously under a value-at-risk (VaR) constraint. Although Wang et al. [2005] had examined this problem, their assumption implied that the insured is risk neutral. Consequently, this study extends Wang et al. [2005] and further considers a more realistic situation where the insured is risk averse. The study derives the optimal insurance contract as a single deductible insurance when the VaR constraint is redundant or as a double deductible insurance when the VaR constraint is binding. Finally, this study discusses the optimal coverage level from common forms of insurances, including deductible insurance, upper-limit insurance, and proportional coinsurance. JEL Classification G22     

A decision theoretic formulation of insurance risk theory

Abstract

In a number of papers Borch has shown how certain insurance problems can be formulated using the concept of utility. (See Borch [3], [4], [5], [6], [7] and [8].) Borch's work is used as a building block in Part I of this report, which presents a Bayesian decision theoretic formulation of some of the main aspects of insurance risk theory. Part I makes use of the concepts of utility and subjective probability. It is admitted that these concepts are more commonly associated with individuals rather than groups of individuals such as insurance companies. However, in this report, we will refer to an insurance company as an individual (albeit a neuter one) and assume that it can quantify its preferences for consequences and its opinions about the occurrence of events. Further, we assume that a company “behaves” according to certain rules of consistent behavior which imply that when presented with several risky courses of action, the company will take the action which has the greatest expected utility. Formal treatments of assumptions that lead to this mode of behavior can be found in Savage [17] and Pratt, Raiffa, and Schlaifer [15].     

A Note on Partial Insurance and the Arrow-Pratt Measure of Risk Aversion

Pratt [1964] establishes that a more risk-averse individual in the Arrow-Pratt sense has a higher compensating risk premium for full insurance, but no comparable result has been established for partial insurance. Ross [1981] shows that a more risk-averse individual in the Arrow-Pratt sense may not be willing to pay more for a reduction in risk in the sense of mean-preserving contraction. We show that a more risk-averse individual in the Arrow-Pratt sense has a higher compensating risk premium for all empirically relevant forms of partial insurance because they induce a reduction in risk in the stronger sense of Bickel and Lemann [1979].JEL Classification No.: D81     

T wave lability: a clue for separating the good from the bad, when ugly

Non-specific T wave abnormalities have challenged both the clinician and the insurance medical director for decades. Distinction between pathologic and physiologic T wave changes often requires costly and time-consuming diagnostic studies. The literature is reviewed on the subject of T wave manipulation by the oral administration of both potassium and glucose, introducing the concept of T wave lability. Based on this concept, a simple technique is suggested which, in many cases, can safely, expeditiously and inexpensively distinguish between organic and functional T wave changes. When employed in the investigation of asymptomatic insurance applicants with unexplained T wave abnormalities but no known cardiovascular or renal disease, this technique appears to be sufficiently reliable to classify the risk posed by non-specific T wave changes without resorting to a sophisticated, lengthy and costly cardiovascular investigation.     

Nachhaltigkeit und Erschwinglichkeit gemeindegetragener Krankenversicherungen in Afrika — Eine Fallstudie aus Nouna Distrikt,Burkina Faso

Many African countries developed national health insurance schemes after independence. However, merely public servants were eligible to subscribe. The majority of the population resides in rural areas where health care services of hospitals and dispensaries were free of charge. The economic crisis of these countries has changed this situation. Currently, almost all health services charge direct user fees so that a severe disease leads to a threat for the entire family of the diseased. Consequently, first community-based health insurances were introduced ten years ago.This paper analyses the effect of these insurance schemes on the service provision for the rural poor with the example of the proposed community-based health insurance in Nouna, Burkina Faso. The insurance can only be sustained if the premium is so high that about 50% of the population cannot afford it. Therefore, this insurance will neither benefit them nor will their situation improve. We have to ask whether a programme that betters the state of the well-off while leaving the condition of the poor unchanged is fair and just. For this purpose different aspects of equity are discussed. The author concludes that the premium-induced exclusion of 50% of the population from the insurance is only acceptable if the privileged use this benefit for economic growth which will finally benefit the poor.     

Public Versus Private Insurance with Dual Theory: A Political Economy Argument

This paper analyzes the political support for public insurance in the presence of a private insurance alternative. The public insurance is compulsory and offers a uniform insurance policy. The private insurance is voluntary and can offer different insurance policies. Adopting Yaari's [Econometrica, 55, 95–115, 1987] dual theory to expected utility (i.e., risk aversion without diminishing marginal utility of income), we show that adverse selection on the private insurance market may lead a majority of individuals to prefer public insurance over private insurance, even if the median risk is below the average risk (so that the median actually subsidizes high-risk individuals). We also show that risk aversion makes public insurance more attractive and that the dual theory is less favourable to a mixed insurance system than the expected utility framework. Lastly, we demonstrate how the use of genetic tests may threaten the political viability of public insurance.     

Islamic Banks,Deposit Insurance Reform,and Market Discipline: Evidence from a Natural Framework

Although it has been intensively claimed that Islamic banks are subject to more market discipline, the empirical literature is surprisingly mute on this topic. To fill this gap and to verify the conjecture that Islamic bank depositors are indeed able to monitor and discipline their banks, we use Turkey as a test setting. The theory of market discipline predicts that when excessive risk taking occurs, depositors will ask higher returns on their deposits or withdraw their funds. We look at the effect of the deposit insurance reform in which the dual deposit insurance was revised and all banks were put under the same deposit insurance company in December 2005. This gives us a natural experiment in which the effect of the reform can be compared for the treatment group (i.e., Islamic banks) and control group (i.e., conventional banks). We find that the deposit insurance reform has increased the market discipline in the Turkish Islamic banking sector. This reform may have upset the sensitivities of the religiously inspired depositors, and perhaps more importantly it might have terminated the existing mutual supervision and support among Islamic banks.     

Optimal insurance contracts without the non-negativity constraint on indemnities: revisited

In the literature on optimal indemnity schedules, indemnities are usually restricted to be non-negative. Keeler [1974] and Gollier [1987] show that this constraint might well bind: insured could get higher expected utility if insurance contracts would allow payments from the insured to the insurer at some losses. This paper extends Collier’s findings by allowing for negative indemnity payments for a broader class of insurers’ cost functions and argues that the indemnity schedule derived here is more appropriate for practical applications (e.g. in health insurance). JEL Classification D80 · D81 · D89     

医疗保险、健康异质性与精准脱贫——基于贫困脆弱性的分析

医疗保险能否有效减少贫困,尚未达成共识。本文利用CHARLS全国调查数据,基于资产度量个体的贫困脆弱性(即陷贫概率),实证分析医疗保险参保行为及其保障水平对贫困脆弱性的影响。研究表明,参与医疗保险和提高医疗保险保障水平的减贫效果都存在健康异质性,对健康状况差的群体有显著的减贫效果,而对健康状况好的群体减贫效果不显著。此外,本文证实了改善劳动供给是医疗保险减贫的重要中介渠道之一。     

Moral intensity,moral awareness and ethical predispositions: The case of insurance fraud

The issue of insurance fraud by consumers continues to perplex insurance firms, costing billions of dollars per year in the United States alone. Some analysts report that 10 per cent or more of property/casualty insurance claims are fraudulent, while less than 20 per cent of fraudulent claims being detected. Consumer attitudes are becoming more tolerant of insurance fraud in recent years. Recognizing that not all insurance fraud situations are created equal, we investigate variability in perceptions of moral intensity in dissimilar insurance padding situations in a 2 (to help others versus to profit self) × 2 (a small credit union versus a large online insurer) model and compared the results between two independent samples (college students/Millennials and an older adult population). We also investigated the impact of ethical predispositions (formalism and utilitarianism) on moral awareness and moral judgment using these four scenarios. The results suggest that the Millennials may exhibit more situationalism and more lenient judgments of collaborative versus unilateral ethical violations. In particular, ‘for self’ versus ‘for others’ comparisons show striking differences between the two age groups. The results add to the growing literature in explaining intra-personal variability in moral decision making.     

面板数据下的线性混合模型及其在车险费率厘定中的应用

精算师在进行车险净保费信度厘定时可采用关于面板数据的线性混合模型,本文采用每次交通事故平均损失额和事故发生频率作为车险净保费的计算指标。利用2008~2012年31个省、市、自治区5年的数据,建立面板数据下的线性混合模型,选取人均地区生产总值、每平方公里人口数、民用汽车拥有量作为解释变量,得到每次交通事故平均损失额和事故发生频率的估计模型,进而得到纯保费估计。这一研究可为车险费率市场化提供一定的理论支持和参考。     

Changes in Background Risk and the Demand for Insurance

The demand for insurance against loss from a particular risky asset is likely to depend on other risks the decision-maker faces. For independently distributed other risks, referred to as background risk, Eeckhoudt and Kimball [1992] determine the effect on insurance demand of introducing background risk. Recently, Eeckhoudt, Gollier, and Schlesinger [1996] determine conditions on preferences such that first- and second-degree stochastic deteriorations in background risk lead to a decrease in the decision-maker's willingness to accept other risks. These results, although formulated in a general decision model, also apply to insurance demand. This article continues analysis of this question by determining the effect on insurance demand of several other general changes in background risk.     

Explaining Insurance Policy Provisions via Adverse Selection

In this article, we show that common insurance policy provisions—namely, deductibles, coinsurance, and maximum limits–can arise as a result of adverse selection in a competitive insurance market. Research on adverse selection typically builds on the assumption that different risk types suffer the same size loss and differ only in their probability of loss. In this study, we allow the severity of the insurance loss to be random and, thus, generalize the results of Rothschild and Stiglitz [1976] and Wilson [1977]. We characterize the separating equilibrium contracts in a Rothschild-Stiglitz competitive market. By further assuming a Wilson competitive market, we show that an anticipatory equilibrium might be achieved by pooling, and we characterize the optimal pooling contract.     

Consumer-centered vs. job-centered health insurance

Most employees and their dependents in the United States have health insurance provided by the employer or labor-management health and welfare fund. In this system, employees and their families lose their health insurance when the breadwinner loses his or her job while, at the same time, a Medicaid beneficiary can lose Medicaid eligibility by getting a job, even a poorly paid one. Most health insurance pays the doctor on the basis of fee-for-service and the hospital on the basis of cost-reimbursement, rewarding both with more revenue for providing more and more costly services. The insured employee has little or no incentive to seek out a less costly provider. There are no rewards for economy in this system. It should be little wonder, then, that health care costs are out of control. There are alternative financing and delivery systems with built-in incentives to use resources economically, but, the author of this article asserts, their ability to compete and attract patients with their superior economic efficiency is blocked by many laws and government programs. The author believes that the most effective and acceptable way to get costs under control, and at the same time achieve universal coverage, would be through a system of fair economic competition. He discusses his Consumer Choice Health Plan proposal and describes how one of the main barriers to competition is today's system of job-linked health insurance.     

Pooling and Separating Equilibria in Insurance Markets with Adverse Selection and Distribution Costs

In the Rothschild-Stiglitz [1976] model of a competitive insurance market with adverse selection, pooling equilibria cannot exist. However in practice, pooling contracts are frequent, notably in health insurance and life insurance. This is due to the fact that distribution costs are nonnegligible and increase rapidly when more contracts are offered. We modify accordingly the Rothschild-Stiglitz model by introducing such distribution costs. We find that, however small these costs may be, they entail possible existence of pooling equilibria. Moreover, in these pooling equilibria, it is the high-risk individuals who are rationed, in the sense that they would be willing to buy more insurance at the current premium/insurance ratio.     

Aufdeckung von Versicherungsbetrug bei Kfz-Schäden mit Hilfe des Benford-Tests

The German Insurance Association estimates a yearly amount of damage of € 1.5?bn to German motor vehicle insurance companies because of systematic fraud by insurance holders. It is supposed that about 10% of submitted claim applications contain manipulated data, therefore insurance companies are forced to complete a detailed and cost intensive case-by-case review of each single application. An alternative method to detect fraud in empiric data is the method of digital analysis based on Benford’s law. The Benford method uses a mathematical law of specific logarithmic distribution attributes of first digits. According to this approach, the data of a Benford set confirm with the expected digit distribution, if the data is not manipulated, whereas fraudulent interventions lead to a deviation from Benford’s law. Hence, until now there has not been any investigation whether the Benford method can also be applied on insurance data. The present article analyses a dataset consisting of more than 120,000 damage claim applications to answer this question as well as to identify the impact of specific characteristics on the probability of fraud contained in claim applications, such as the repair of the vehicle in a franchised or an independent workshop, the vehicle brand or the examination by insurance companies experts. Indeed it could be shown that Benford’s Law is only applicable on second digits of insurance data, but delivers very strong results here: All results of the considered characteristics could be verified by plausible arguments. For this reason insurance companies can benefit from making use of the Benford method to identify those claim applications with a high probability of fraud, which should then be reviewed in more detail so that resources can be allocated in a much more cost efficient way.     

Alternative Solutions to Underinvestment, Under Equity and Credit Rationing

We compare alternative solutions to underinvestment (UI) problems in firms subject to limited access to equity markets, interest ceilings, and constraints on the volume of debt. Collaterals (assets or compensating balances) and credit insurance ('regular' or 'outcome' insurance whereby the premium is paid at the end of the insurance period) are compared on the basis to their costs and their effective use of financial sources. It is shown that when there is no moral hazard problem, credit insurance is the most effective instrument. Otherwise, 'outcome' insurance program is the most effective one.     

Alternative Solutions to Underinvestment, Under Equity and Credit Rationing

We compare alternative solutions to underinvestment (UI) problems in firms subject to limited access to equity markets, interest ceilings, and constraints on the volume of debt. Collaterals (assets or compensating balances) and credit insurance ('regular' or 'outcome' insurance whereby the premium is paid at the end of the insurance period) are compared on the basis to their costs and their effective use of financial sources. It is shown that when there is no moral hazard problem, credit insurance is the most effective instrument. Otherwise, 'outcome' insurance program is the most effective one.     

Opportunities for banks to cross-sell insurance products in Greece

The paper aims to identify whether or not there are opportunities for banks in Greece effectively to cross-sell insurance products through their branch network. In addition, it seeks to investigate the areas of insurance product portfolio that could have a better potential to be distributed by Greek banks, and to identify the profile of potential customers. For this reason a questionnaire was designed, and was completed by 720 bank customers. The analysis showed that the greatest opportunity comes from the fact that consumer awareness of the offering of insurance products by banks is low in contrast to their willingness to use banks as insurance products providers, which is very high. Additionally, there are indications that based on consumer attitudes, there are identifiable market segments which are more attractive. In conclusion, the paper discusses the managerial implications of the findings and proposes suggestions for further research.     

《社会保险法》实施对外出农民工社会保险参保率的影响研究

本文采用2016年全国流动人口动态调查数据,运用截面双重差分法研究《社会保险法》实施对外出农民工社会保险参保率的影响。研究表明,《社会保险法》的实施显著提高了在非公共部门就业的外出农民工(2011年时16~25岁)的社会保险参保率。进一步研究发现,《社会保险法》对受教育程度较低的外出农民工以及市内跨县并在非公共部门就业的外出农民工的社会保险参保率的影响更显著。建议政府为农民工继续教育设立畅通渠道,提高其人力资本素质。本文有利于帮助政府科学明确就业保护法规的保护对象,为进一步完善就业保护法规提供参考依据。