Pricing for Multiline Insurer: Frictional Costs,Insolvency, and Asset Allocation

This article examines multiline insurance pricing based on the contingent claim approach in a limited liability and frictional costs environment. Capital allocation is based on the value of the default option, which satisfies the realistic assumption that each distinct line undertakes a pro rata share of deficit caused by insurer insolvency. Premium levels, available assets, and default risk interact with each other and reach equilibrium at the fair premium. The assets available to pay for liabilities are not predetermined or given; instead, the premium income and investment income jointly influence the available assets. The results show that equity allocation does not influence the overall fair premium. For a given expected loss, the premium-to-expected-loss ratio for firms offering multiple lines is higher than that for firms only offering a single line, due to the reduced risk achieved through diversification. Premium-to-expected-loss ratio and equity-to-expected-loss ratio vary across lines. Lines having a higher possibility or claim amount not being paid in full exhibit lower premium-to-expected-loss ratio and higher equity-to-expected-loss ratio. Positive correlation among lines of business results in lower premium-to-expected-loss ratio than when independent losses are assumed. Positive correlation between investment return and losses reduces the insolvency risk and leads to a higher premium-to-expected-loss ratio.     

The Bankruptcy Cost of the Life Insurance Industry Under Regulatory Forbearance

Abstract

In this study the Taiwan Insurance Guaranty Fund (TIGF) is introduced to investigate the ex ante assessment insurance guaranty scheme. We study the bankruptcy cost when a financially troubled life insurer is taken over by TIGF. The pricing formula of the fair premium of TIGF incorporating the regulatory forbearance is derived. The embedded Parisian option due to regulatory forbearance on fair premiums is investigated. The numerical results show that leverage ratio, asset volatility, grace period, and intervention criterion influence the default costs. Asset volatility has a significant effect on the default option, while leverage ratio is shown to aggravate the negative influence from the volatility of risky asset. Furthermore, the numerical analysis concludes that the premium for the insurance guaranty fund is risk sensitive and that a risk-based premium scheme could be implemented, hence, to ease the moral hazard.     

Can Bonus‐Malus Allieviate Insurance Fraud?

Traditionally, insurance companies attempt to reduce (or even eliminate) fraud via audit strategies under which claims may be investigated at some cost to the insurer, with a penalty imposed upon insureds who are found to report claims fraudulently. However, it is also clear that, in a multiperiod setting, bonus‐malus contracts (increases in subsequent premiums whenever a claim is presented) also provide an incentive against fraud. In this article, we consider a model in which, conditional upon the client renewing his contract, the only mechanism used to combat fraud is bonus‐malus. In this way, our model provides the opposite pole to the pure audit model. We show that in our simplified setting there exists a bonus‐malus contract that will eliminate all fraud in all periods, while guaranteeing nonnegative expected profits to the insurer and participation by the insured. We also consider the dynamics of the solution, the effect of an increase in risk aversion on the solution, and the welfare implications.     

On the medical loss ratio (MLR) and sticky selling general and administrative costs: Evidence from health insurers

The Patient Protection and Affordable Care Act of 2010 (ACA) imposed an important constraint on health insurers: if the medical loss ratio (MLR), determined as the ratio of claims paid to premiums collected, declined below certain legislative targets, the insurer would be obliged to rebate a portion of the premiums to the customer. It might be expected that this increase in the MLR would result in a decrease in premium dollars available to cover selling, general and administrative costs (SG&A) and a concomitant decrease in profits. However, there is earlier evidence that SG&A “cost stickiness” presents a counter-effect in this instance: namely, that an increase in SG&A costs per each dollar of revenue increase is more than the magnitude of a decrease in SG&A costs per each dollar of revenue decrease. In this context, this paper offers the first preliminary evidence of the impact of the MLR regulatory change on SG&A cost stickiness in the health insurance industry.Applying the Anderson et al. (2003) methodology, our sample of publicly-traded health insurers shows evidence of significant mitigation of the SG&A cost stickiness after the implementation of the ACA medical loss ratio rules and that in periods of revenue declines, SG&A costs decreased more significantly post-ACA than pre-ACA. These results further illustrate the tension created by regulatory policy designed to improve healthcare cost efficiency and its impact on the profit seeking activities of for-profit healthcare enterprises. Thus, this paper contributes to both healthcare and accounting literature by documenting a significant effect of regulatory policy on managerial decisions regarding cost control.     

“Analysis of Incremental Returns of Canadian Mutual Funds”, J. F. Carrière; C. F. Hill,April 2001

Abstract

The determination and allocation of economic capital is important for pricing, risk management, and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed-form results for the complete markets, arbitrage-free allocation of the insurer default option value, or insolvency exchange option, to lines of business for an insurer balance sheet. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multiline insurer. We discuss and illustrate other methods of capital allocation, including Myers-Read, and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line.     

Risk-based capital standards, deposit insurance, and procyclicality

This article shows that risk-based deposit insurance premiums generate smaller procyclical effects than do risk-based capital requirements. Thus, Basel II's procyclical impact can be reduced by integrating risk-based deposit insurance. If deposit insurance is structured as a moving average of contracts, its procyclical effects can be decreased further. Empirical illustrations of this are presented for 42 banks over the period 1987 to 1996. The results confirm that lengthening the contracts' maturities intertemporally smooths premiums but raises the average premium level needed to compensate the insurer for greater systematic risk. The distribution of risk-based premiums across banks is skewed.     

Risk-Based Premiums for Insurance Guaranty Funds

Insurance guaranty funds have been adopted in all states to compensate policyholders for losses resulting from insurance company insolvencies. The guaranty funds charge flat premium rates, usually a percentage of premiums. Flat premiums can induce insurers to adopt high-risk strategies, a problem that can be avoided through the use of risk-based premiums. This article develops risk-based premium formulas for three cases: a) an ongoing insurer with stochastic assets and liabilities, b) an ongoing insurer also subject to jumps in liabilities (catastrophes), and c) a policy cohort, where claims eventually run off to zero. Premium estimates are provided and compared with actual guaranty fund assessment rates.     

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.     

Optimal proportional reinsurance with a loss-dependent premium principle

ABSTRACT

Empirical studies suggest that many insurance companies recontract with their clients on premiums by extrapolating past losses: a client is offered a decrease in premium if the monetary amounts of his claims do not exceed some prespecified quantities, otherwise, an increase in premium. In this paper, we formulate the empirical studies and investigate optimal reinsurance problems of a risk-averse insurer by introducing a loss-dependent premium principle, which uses a weighted average of history losses and the expectation of future losses to replace the expectation in the expected premium principle. This premium principle satisfies the bonus-malus and smoothes the insurer's wealth. Explicit expressions for the optimal reinsurance strategies and value functions are derived. If the reinsurer applies the loss-dependent premium principle to continuously adjust his premium, we show that the insurer always needs less reinsurance when he also adopts this premium principle than when he adopts the expected premium principle.     

Medicaid coverage expansions and liability insurance

Do changes in the population covered by health insurance affect liability insurers, who compensate billions of dollars in medical claims each year? We examine this question by exploiting the selective rollout across states of Medicaid expansions under the Affordable Care Act. Using data on insurer losses across a range of insurance lines, and employing a triple‐difference research design that contrasts states, years, and lines of insurance, we demonstrate that coverage expansions reduce auto liability and workers’ compensation outlays by 6–11 percent, but do not measurably impact other lines of insurance. Our analysis provides some of the first evidence regarding the use of the tort system particularized to the low‐income population and is the first to consider the impacts of health insurance on medical professional liability and commercial auto insurance claims.     

Unallocated loss adjustment expense reserving

In non-life insurance, the provision for outstanding claims (the claims reserve) should include future loss adjustment expenses, i.e. administrative expenses to settle the claims, and therefore we have to estimate the expected Unallocated Loss Adjustment Expenses (ULAE) – expenses that are not attributable to individual claims, such as salaries at the claims handling department. The ULAE reserve has received little attention from European actuaries in the literature, supposedly because of the lack of detailed data for estimation and evaluation. Having good estimation procedures will, however, become even more important with the introduction of the Solvency II regulations, which require unbiased estimation of future cash flows for all expenses. We present a model for ULAE at the individual claim level that includes both fixed and variable costs. This model leads to an estimate of the ULAE reserve at the aggregate (line-of-business) level, as demonstrated in a numerical example from a Swedish non-life insurer.     

Reinsurance decisions in life insurance: An empirical test of the risk–return criterion

Recent studies have analyzed optimal reinsurance contracts within the framework of profit maximization and/or risk minimization. This type of framework, however, does not consider reinsurance as a tool for capital management and financing. In the present paper, we consider different proportional reinsurance contracts used in life insurance (viz., quota-share, surplus, and combinations of quota-share and surplus) while taking into account the insurer's capital constraints. The objective is to determine how different reinsurance transactions affect the risk/reward profile of the insurer and whether factors, such as claims severity, premiums, and insurer's risk appetite, influence the choice of a proportional reinsurance coverage. We compare each reinsurance structure based on actual insurance company data, using the risk–return criterion. This criterion determines the type of reinsurance that enables insurer to retain the largest underwriting profits and/or minimize the risk of the retained claims while keeping the insurer's risk appetite constant, assuming a given capital constraint. The results of this study confirm that the choice of reinsurance arrangement depends on many factors, including risk retention levels, premiums, and the variance of the sum insured values (and therefore claims). As such, under heterogeneous insurance portfolio single type of reinsurance arrangement cannot maximize insurer's returns and/or minimize the risk, therefore a combination of different reinsurance coverages should be employed. Hence, future research on optimal risk management choices should consider heterogeneous portfolios while determining the effects of different financial and risk management tools on companies' risk–return profiles.     

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.     

The Effects of Regulated Premium Subsidies on Insurance Costs: An Empirical Analysis of Automobile Insurance

State regulation of rates is sometimes used as a means to make automobile insurance more affordable to consumers by restricting insurer profits and pricing practices. Incentive distortions arising from this type of rate regulation might lead to higher accident rates and higher insurance loss costs. Annual state‐level panel data for the time period 1980–1998 are used to investigate these effects, using empirical methods that recognize the endogenous determination of states’ regulatory choices. Results suggest that rate regulation that systematically suppresses (some or all) drivers’ insurance premiums is associated with significantly higher average loss costs and higher insurance claim frequency.     

临时保险制度：赔付理由、期间及其限制

我国《保险法》未规定临时保险制度,本文建议,我国的临时保险制度应当分为强制临时保险与自愿临时保险两种,在保险人预收保险费的情况下,根据履行提前、对价平衡、合理期待等理论,保险人应当对临时保险事故予以赔付,此种临时保险的期间自投保人交付保险费之时起算,于正式保险生效之时或投保人收到拒保通知书并由保险人退还保险费之时终止;...     

Market Pricing of Deposit Insurance

We provide an approach to the market valuation of deposit insurance that is based on reduced-form methods for the pricing of fixed-income securities under default risk. By reference to bank debt prices as well as qualitative-response models of the probability of bank failure, we suggest how a risk-neutral valuation model for deposit insurance can be applied both to the calculation of fair-market deposit insurance premia and to the valuation of long-term claims against the insurer.     

Reinsurance premium principles based on weighted loss functions

ABSTRACT

In this paper, we propose new reinsurance premium principles that minimize the expected weighted loss functions and balance the trade-off between the reinsurer's shortfall risk and the insurer's risk exposure in a reinsurance contract. Random weighting factors are introduced in the weighted loss functions so that weighting factors are based on the underlying insurance risks. The resulting reinsurance premiums depend on both the loss covered by the reinsurer and the loss retained by the insurer. The proposed premiums provide new ways for pricing reinsurance contracts and controlling the risks of both the reinsurer and the insurer. As applications of the proposed principles, the modified expectile reinsurance principle and the modified quantile reinsurance principle are introduced and discussed in details. The properties of the new reinsurance premium principles are investigated. Finally, the comparisons between the new reinsurance premium principles and the classical expectile principle, the classical quantile principle, and the risk-adjusted principle are provided.     

先行支付制度法理分析

从社会保险法理看,社会保险基金对第三人侵权造成的保险损害承担保险给付义务,在履行保险给付义务之后,保险人依法获得保险代位权;工伤保险基金对未缴纳保险费的单位职工工伤损害承担保险赔偿责任.我国《社会保险法》确立的先行支付制度,否定相关社会保险基金在该情形下的保险赔偿义务.这不仅冲击了社会保险法理,也违背了社会保险法的基本原则,而且给司法实践造成一定困扰.明确相关保险基金先行支付义务和求偿权的实质,是该制度正常运用的基础.     

From T-Bills to Stocks: Seasonal Anomalies Revisited

This paper employed eleven data series which consist of stocks, bonds, bills, equity premiums, term premiums, and various default premiums to investigate whether January seasonality reported in existing literature is robust across different states of the economy as this has important trading implications. For the periods 1926–1990, small stocks, small stock premiums, low grade bonds, and default premiums (spread between high grade, low grade and government bonds) reveal January seasonality and that the seasonality is robust across different states of the economy except for low grade bond returns and default premiums. January seasonality for low grade bond returns and low grade bond default premiums are primarily driven by results found during periods of economic expansion. Overall, January seasonality is more evident during the economic expansion periods although the magnitude of default premiums is larger during periods of economic contraction. Furthermore, prior findings of strong summer equity returns are primarily driven by the results found during the periods of economic contraction. It is also found that equity returns are generally higher during periods of economic expansion.