Who Obtains Greater Discounts on Automobile Insurance Premiums?

Insurance purchasers obtain varied discounts for insurance. This paper examines what drives these differences, specifically whether the loss probability and the wealth of the insured affect the size of the premium discount in automobile insurance. To describe a bargain between a client and an insurer over premiums and coverage, we first develop a sequential insurance bargaining game where the client has an outside option to bargain with another insurer. We find that the equilibrium involves full coverage and, based on the results of comparative statics, we propose hypotheses regarding the effects of the loss probability and the wealth of the insured on the size of the premium discount. We then use a unique data set of 85,806 observations of Taiwanese automobile liability insurance for property damage to empirically test the predictions. After controlling for underwriting and macroeconomic variables, we find that both (1) the insured with a lower claim probability (as a proxy for the insured with a lower loss probability) and (2) the insured with a higher salvage value car (as a proxy for the wealthier insured) receive a greater premium discount. These results support our theoretical results.     

Insurance Market Effects of Risk Management Metrics

We extend the classical analysis on optimal insurance design to the case when the insurer implements regulatory requirements (Value-at-Risk). Presumably, regulators impose some risk management requirement such as VaR to reduce the insurers’ insolvency risk, as well as to improve the insurance market stability. We show that VaR requirements may better protect the insured and improve economic efficiency, but have stringent negative effects on the insurance market. Our analysis reveals that the insured are better protected in the event of greater loss irrespective of the optimal design from either the insured or the insurer perspective. However, in the presence of the VaR requirement on the insurer, the insurer's insolvency risk might be increased and there are moral hazard issues in the insurance market because the optimal contract is discontinuous.     

Insurance Contract Design When the Insurer Has Private Information on Loss Size

This article examines the optimal indemnity contract in an insurance market, when the insurer has private information about the size of an insurable loss. Both parties know whether or not a loss occurred, but only the insurer knows the true value of the loss and/or to what extent the losses are covered under the policy. The insured may verify the insurer's loss estimate for a fixed auditing cost. The optimal contract reimburses the auditing costs in addition to full insurance for losses less than some endogenous limit. For losses exceeding this limit, the contract pays a fixed indemnity and requires no monitoring. The optimal contract is compared with the contracts obtained in cases where it is only the insured who can observe the loss size.
     

Risk-based capital for credit insurers with business cycles and dynamic leverage

This paper develops a risk-based capital pricing model for credit insurance portfolios held by a vulnerable insurer. The model accounts for business cycles using a two-state Markov switching model, and allows for dynamic leverage adjustment by the insured firms. The new proposed model, which incorporates risk-based capital practice, is better for both the insurer and the insured firms. Based on the risk-adjusted performance metric, we found that the insurer is better off insuring short- and medium-term loans in expansion and steady states, while it is better off backing both short- and long-term loans in recessions. Our results also emphasize that macroeconomic uncertainty significantly impairs the creditworthiness of the insurer and insured firms.     

Die Haftpflichtversicherung nach der VVG-Reform

The reform of the German Insurance Contract Act (Versicherungsvertragsgesetz, ?VVG“) also targets key aspects of third-party liability insurance. The changes go beyond the findings made by both the courts and legal authorities to date.Compulsory insurance aside, the law still provides that an injured third party has no standing to assert a claim directly against the tortfeasor’s liability insurer. The tortfeasor may assign its indemnity claim against the insurer solely to the injured third party and may no longer be precluded from doing so under the General Insurance Conditions (AVB). Consequently, the tortfeasor’s indemnity claim against the insurer effectively becomes a pecuniary claim. This is criticised by the insurance industry particularly with regard to eliminating the prohibition against acknowledgment and satisfaction of claims.In the future, third parties will be able to assert claims directly against the tortfeasor’s insurer and this will be the case for compulsory insurance across the board. Provisions currently in effect in the motor vehicle liability insurance industry will be carried over to the entire compulsory insurance sector. Compulsory insurance does permit agreements involving self-deductibles. However, such agreements are generally effective only as between the insurer and the tortfeasor inter se, i.e. they are not effective as against third parties — in contrast to valid disclaimers of risk.Another change in compulsory insurance is the hierarchy of claims for compensatory damages and relief in the event the insured amount is inadequate. Specifically, the hierarchy gives preference to individual claims of injured parties which are not otherwise covered, such as claims for pain and suffering.The prohibition against the retroactive loss of provisional coverage for failure to pay the first premium, which had been criticised primarily by motor vehicle liability insurers, has been omitted in the Government bill.     

Wird der vom Regierungsentwurf eines VVG geplante Direktanspruch des Geschädigten gegen den Pflichthaftpflichtversicherer ein stumpfes Schwert? Zur Notwendigkeit eines Informationsanspruchs des Geschädigten in der neuen Pflichthaftpflichtversicherung

The amendment of the German Act on Insurance Contracts comprises a number of substantial modifications regarding liability insurance. The most important modification is the introduction of a direct claim against the insurer with regard to all compulsory insurances. Such a direct claim is up to now only known from the motor vehicle liability insurance. Yet, a direct claim will be advantageous for the aggrieved claimant only if he manages to identify the proper insurer. As a result of the structural differences to the motor vehicle liability insurance the act of identifying the insurer is almost utterly impossible for the claimant without any help by the insured. Thus the claimant must also be given a claim against the insured to be furnished with all necessary information regarding the insurer. This right originates from sec. 242 of the German Civil Code.     

从博弈论看保险市场信息不对称的本质及规范举措

博弈论是研究信息不对称问题的一种有效方法。保险业作为信息不对称最为集中的行业，保险人与被保险人之间存在着严重的信息不对称，特别是被保险人的逆向选择、道德风险和保险人的违规操作等现象普遍存在，长期困扰着保险界。     

Grenzen der Auskunfts- und Belegpflicht in der D&O Versicherung

A large number of claims brought under German D&O insurance regard Insured vs. Insured cases, i.e. claims brought by the company against its own directors and officers (Executive Directors, Supervisory Board Members etc.). After notification of and examination by the insurer of such an insured event, the insurer will in most cases opt to grant the insured defence cover in order to fight off the claim. The insurer hereby expresses that it regards the claim of the company (= its own policyholder) against the board member (= the insured) to be without merit. This situation—where the policyholder is at the same time the damaged party—though typical under (German) D&O-policies is uncommon for liability insurance cover in general. It, thus, raises the issue as to the limits of the policyholder’s duty to disclose information. The scope of said obligation is not unlimited. It rather has to be ascertained pursuant to Sect. 31 VVG (German Insurance Contract Act), by taking into account the policyholder’s interests in commercial and industrial confidentiality and the burden of poof as provided by Sect. 93 para. 2 AktG (German Stock Companies Act). In case legal proceedings ensue between the company and the insured, and, as a consequence, the insurer exercises its obligation to conduct the case for the insured or the insurer joins the lawsuit on the side of the insured (by declaring a Third Party Notice [Streiverkündung]), the insurer clearly becomes an adversary to the company. Under such circumstances, the company is irrevocably released from its duty to disclose information.     

The benefit of life insurance contracts with capped index participation when stock prices are subject to jump risk

We analyze the benefit to the insured of newly traded, innovative life insurance contracts. On a sequence of yearly reference days, the insured can choose between a guaranteed return (linked to the insurer’s asset result) and a capped index participation. The cap is adjusted at the beginning of each year such that both alternatives have the same value and the option to select is costless (product structuring condition). We point out that this condition cannot always be met. If the guaranteed return exceeds the upper bound of the capped index participation, the insurer can make a side profit. We show that a rather low insurance result also implies a rather low stock exposure, even if the insured opts for the index participation. Concerning the impact of the index dynamics, we emphasize that it is important to distinguish between jump and diffusion risk because the pricing of jump risk has an impact on cap rates that can be offered to an insured. Finally, we show that the optimal decision strategy of a CRRA investor implies an index selection even if it is unfairly priced such that the insurer indeed makes a side profit.     

Optimal Insurance Under the Insurer's VaR Constraint

In this paper, we impose the insurer's Value at Risk (VaR) constraint on Arrow's optimal insurance model. The insured aims to maximize his expected utility of terminal wealth, under the constraint that the insurer wishes to control the VaR of his terminal wealth to be maintained below a prespecified level. It is shown that when the insurer's VaR constraint is binding, the solution to the problem is not linear, but piecewise linear deductible, and the insured's optimal expected utility will increase as the insurer becomes more risk-tolerant. Basak and Shapiro (2001) showed that VaR risk managers often choose larger risk exposures to risky assets. We draw a similar conclusion in this paper. It is shown that when the insured has an exponential utility function, optimal insurance based on VaR constraint causes the insurer to suffer larger losses than optimal insurance without insurer's risk constraint.     

Exotic unit-linked life insurance contracts

This article integrates aspects of traditional insurance with advances in financial economics, yielding proper valuation and premium assessments of insurance benefits linked to various financial assets. Several new types of unit-linked life insurance contracts are discussed, with substantial potential for real-life applications. Compared to usual unit-linked products, these contracts offer added flexibility and/or altered exposure to financial risk for the insured and/or the insurer. The single premiums of these policies are calculated as expectations under a risk-adjusted probability measure (equivalent martingale measure), satisfying no-arbitrage conditions in financial markets.     

Die vorvertragliche Anzeigepflicht: Empfehlungen für ein europäisches Versicherungsvertragsrecht

In all European legal systems, the pre-contractual duty of disclosure is the most fundamental duty of the insured. Therefore, it is also the focal point of the debate about the harmonization of insurance contract law in Europe. As this discussion has recently gained momentum, this contribution provides a comparative overview of the rules regulating the duty of disclosure in different European countries and submits recommendations for its design in a European insurance contract law. More specifically, it is recommended that the insured should be required to disclose any fact material to the risk, that is either known to him or that he can be assumed to know. In case of breach, the insurer should either be entitled to repudiate the contract ab initio, to cancel the contract for the future or to claim damages depending on whether and to what degree the insured is at fault and depending on whether there is a causal connection between the non-disclosed fact and the formation of the contract or the occurrence of the insured event.     

新保险法热点问题之中港比较

比较大陆和香港两地保险实践,会发现许多热点问题在大陆地区和香港地区之法律规制仍存在较大差异.伴随着大陆地区保险市场的逐步成熟,大陆保险法律体系的完善亦可借鉴香港地区相关理念和做法,充分发挥行业自律的重要作用,并逐步推进以市场行为为中心的监管模式向以偿付能力为中心的监管模式转变.     

A Continuous-Time Optimal Insurance Design with Costly Monitoring

We provide a theoretical and numerical framework to study optimal insurance design under asymmetric information. We consider a continuous-time model where neither the efforts nor the outcome of an insured firm are observable to an insurer. The insured may then cause two interconnected information problems: moral hazard and fraudulent claims. We show that, when costly monitoring is available, an optimal insurance contract distinguishes the one problem from the other. Furthermore, if the insured’s downward-risk aversion is weak and if the participation constraint is not too tight, then a higher level of the monitoring technology can mitigate both problems.     

Efficient Insurance Contracts under Epsilon-Contaminated Utilities

This paper analyses the qualitative properties of optimal contracts when agents have multiple priors and are uncertainty averse in an infinite state space framework. The case of the epsilon-contamination of a given prior, a basic tool in robustness theory is fully developped. It is shown that if both agents have strictly concave utility index, then if the insurer is less uncertainty averse than the insured, he provides a full insurance contract above a deductible for high values of the loss.     

Insurance law and incomplete contracts

We analyze how insurance law can mitigate moral hazard by allowing insurers to reduce or cancel coverage in some circumstances. We consider an incomplete contract setting in which the insurer may obtain information related to the policyholder's behavior through a costly audit of the circumstances of the loss. Court decisions are based on a standard of proof such as the balance of probabilities. We show that an optimal insurance law brings efficiency gains compared to the no-audit case. We also highlight the conditions under which the burden of proof should be on the insured, provided that insurers are threatened with sanctions for bad faith.     

Insurance premiums and default risk in mutual insurance

Abstract

Two types of default risk are discussed in the article: The traditional “probability of ruin” (insurer being unable to meet his obligations) and a “perceived probability of ruin” (the probability of the insured being affected by ruin). The explicit relationship between these probabilities on the actuarial loading factors of a mutual insurer were developed. The explicit mathematical formulae obtained for these complex relationships were followed also by numerical results. A second concept presented in the paper is related to the idea of actuarially fair premiums. It is shown that the premium must also be a function of the payments of the other insured as well as their claim distributions, reflecting thereby the simultaneity and mutual dependence of the insured.     

Ex ante loss control by insurers: Public interest for higher profit

This article examines the incentives of an insurer to modify loss distributions prior to the sale of insurance. While actions such as lobbying Congress for mandatory airbags in automobiles are undertaken by insurers for the stated purpose of reducing the aggregate loss in society, they also change the nature of the risk being insured and, hence, affect the profitability of insurance sales. For the case of loss prevention (reducing the probabilty of a loss), insurers do not always have an incentive to invest in loss control. For loss reduction (reducing the severity of any loss that does occur), the incentive is to reduce the size of small losses while simultaneously increasing the size of large losses. Venezian Associates     

Optimal insurance and reinsurance policies chosen jointly in the individual risk model

The paper studies the so-called individual risk model where both a policy of per-claim insurance and a policy of reinsurance are chosen jointly by the insurer in order to maximize his/her expected utility. The insurance and reinsurance premiums are defined by the expected value principle. The problem is solved under additional constraints on the reinsurer’s risk and the residual risk of the insured. It is shown that the solution to the problem is the following: The optimal reinsurance is a modification of stop-loss reinsurance policy, so-called stop-loss reinsurance with an upper limit; the optimal insurer’s indemnity is a combination of stop-loss- and deductible policies. The results are illustrated by a numerical example for the case of exponential utility function. The effects of changing model parameters on optimal insurance and reinsurance policies are considered.     

论责任保险被保险人“怠于请求”行为之司法界定

2009年新修订的《保险法》第65条增加规定,赋予保险事故受害第三者在一定条件下对保险人的直接赔偿请求权,这是我国责任保险法律制度的进步。然而,《保险法》对被保险人“怠于请求”行为的认定并未作具体明确的规范,这必将使司法实践对此类案件的处理陷入困境。在目前条件下,为切实保证责任保险制度保护受害第三者利益立法目的之实现,...