Remarks on the Mossin Theorem

We establish several new results regarding the Mossin Theorem under both nonrandom initial wealth and random initial wealth. For the nonrandom initial wealth case, we show that the Mossin Theorem holds for any constrained class of insurance contracts whose maximum coverage provides full coverage of the potential loss. This result not only settles an open conjecture, but also provides a unified treatment for extant varieties of the Mossin Theorem. For the random initial wealth case, we give a thorough study of the upper-limit insurance. In particular, we show that (1) for a fair premium, the Generalized Mossin Theorem for coinsurance does not hold for upper-limit insurance, and (2) for an unfair premium, partial insurance will always be optimal, regardless of the risk preference of the individual and the dependence structure between the random loss and the random initial wealth.     

A note on Mossin’s theorem for deductible insurance given random initial wealth

Mossin’s theorem for deductible insurance given random initial wealth is re-examined. For a fair premium, it is shown that a necessary and sufficient condition, in the spirit of the Generalized Mossin Theorem for coinsurance, is impossible using the notion of expectation dependence. Next, it is established that for a fair premium, full insurance will be optimal for a risk-averse individual if the random loss and the random initial wealth are negative quadrant dependent, improving upon an extant result in the literature. In view of a set of examples given in this paper, such a sufficient condition cannot be obtained using the notion of expectation dependence. Finally, for an unfair premium, it is shown that partial insurance will always be optimal, irrespective of the risk preference of the individual as well as the dependence structure between the random loss and the random initial wealth.     

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.     

Mossin's Theorem for Upper-Limit Insurance Policies

Although Mossin's Theorem (“full insurance with a fair premium and less‐than‐full coverage with a proportional premium loading”) is well known for the classes of coinsurance contracts and for deductible‐insurance contracts, it has not been proven for the class of upper‐limit insurance contracts. This article provides a proof for this case.     

The Effect of Pre-commitment and Past-Experience on Insurance Choices: An Experimental Study

This paper reports results from an experimental study that investigates insurance behaviors in low-probability, high-loss risk situations. The study reveals that insurance behaviors may depend on the length of the commitment period of insurance policies, namely the period during which individuals commit themselves to maintain the same insurance decision. The results of this study also seem to support the predictions of the Dual Theory concerning the demand for co-insurance policies, that is to say the preference of individuals for extreme (null or full) levels of insurance coverage. This study also suggests that prior risk occurrences influence subsequent insurance choices. The paper provides a new possible explanation about the puzzling fact that people usually fail to obtain insurance against disaster-type risks such as natural disasters, even when premiums are close to actuarially fair levels.     

Consumers’ collision insurance decisions: a mental models approach to theory evaluation

Using interviews with 74 drivers, we elicit and analyze how people think about collision insurance coverage and decide whether to buy coverage, and if so, what deductible level to carry. We compare respondents’ judgments and behaviors to predictions of three models: baseline expected utility (EU) theory, which predicts that insurance is an inferior good, meaning more wealthy people buy less; a modified EU model, which incorporates income constraints and suggests that property insurance is a normal good, meaning more wealthy people buy more; and a mental accounting model which predicts that consumers budget income across consumption categories. The results suggest they purchase insurance as a normal good, guided by a cognitive model that emphasizes budget constraints. Verbal reports reveal a desire to balance two conflicting goals in deductible decisions: keeping premiums ‘affordable’ and keeping deductible level ‘affordable.’ Thus, wealth does not distinguish people by risk aversion, but by ability to pay. In other words, the behavior of less wealthy people is not driven by greater risk aversion, but by their lesser ability to pay, both now and later. We find that a simple heuristic using only vehicle value accounts for most decisions of whether to purchase optional collision coverage: out of 45 respondents who did not have loans on their vehicles, 90% of those with vehicles worth more than $1000 carried collision coverage, while less than 30% of those with lower‐valued vehicles did.     

“Skewness and Stock Option Prices”, Hans Gerber and Bruno Landry,July 1997

We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among life insurance, income, and the probability of dying and thus losing that income. For insurance purchased via a single premium or premium payable continuously, we explicitly determine the optimal death benefit. We show that if the premium is determined to target a specific probability of loss per policy, then the rates of consumption are identical under single premium or continuously payable premium. Thus, not only is equivalence of consumption achieved for the households under the two premium schemes, it is also obtained for the insurance company in the sense of equivalence of loss probabilities.     

The Demand for Insurance With an Upper Limit on Coverage

The demand for insurance is examined when the indemnity schedule is subject to an upper limit. The optimal contract is shown to display full insurance above a deductible up to the cap. Some results derived in the standard model with no upper limit on coverage turn out to be invalid; the optimal deductible of an actuarially fair policy is positive and insurance may be a normal good under decreasing absolute risk aversion. An increase in the upper limit would induce the policyholder with constant absolute risk aversion to reduce his or her optimal deductible and therefore this would increase the demand for insurance against small losses.     

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 comparative statics of deductible insurance in expected- and non-expected-utility theories

This paper identifies comparative statics results for insurance contracts that distinguish between various models of decision making under risk—specifically, expected utility, rank-dependent expected utility, and weighted utility. Insurance contracts offer full coverage above a deductible. Firms offer premium schedules that give the premium charged as a function of the deductible; households choose both an insurance company and a deductible to maximize utility. A competitive equilibrium requires zero expected profit for firms. We identify changes in the distribution of losses such that the optimal deductible increases for utility representations in a particular class but decreases for some representations outside that class. We give results both for the demand for insurance, as well as for the equilibrium contract.     

The impact of a partial borrowing limit on financial decisions

We consider a consumption, investment, life insurance, and retirement decision problem in which an economic agent is allowed to borrow against only a part of future income. The closed-form solution is attained by applying a dual approach that directly imposes the conditions for the borrowing limit on a dual value function. We provide analytic comparative statics for optimal strategies with rigorous proofs. It is confirmed that a more stringent borrowing limit leads to less consumption and less life insurance purchase. However, even with a tighter borrowing limit, an agent with weak incentive to retire can invest more when the wealth level is high enough. We also show that a more stringent borrowing limit can delay or hasten the optimal retirement timing depending on the agent's current wealth level.     

Optimal Insurance Policy Indemnity Schedules With Policyholders’ Limited Liability and Background Risk

This article makes two contributions to the insurance literature by studying optimal insurance policy indemnity schedules with policyholders’ limited liability and background risk. First, generalizing a prominent approach by Huberman, Mayers, and Smith (1983), it is shown that a welfare subsidy in the case of a ruinous loss may make the insurance premium “overly fair” for nonbankrupting losses and full insurance for this event becomes optimal. Second, introducing correlated background risk into this limited liability framework relativizes or even turns results by Doherty and Schlesinger (1983) as to the impact of background risk on optimal coverage into its opposite.     

A Study of the Interaction of Insurance and Financial Markets: Efficiency and Full Insurance Coverage

The first contribution of this article is to provide a framework, a model together with a corresponding equilibrium notion, suitable for the study of the interaction between insurance and dynamic financial markets. Our central result is that in equilibrium risk‐averse agents purchase full insurance coverage, despite unfair insurance prices. We identify three conditions that explain this result: (1) insurance contracts are priced competitively, (2) financial prices include a risk premium only for undiversifiable risk, and (3) financial markets are effectively complete. An implication is that in this model disasters can be insured by fully assessable stock insurance companies.     

The design of an optimal insurance contract for irreplaceable commodities

This paper discusses optimal insurance contract for irreplaceable commodities. To describe the dual impacts on individuals when a loss occurs to the insured irreplaceable commodities, we use a state-dependent and bivariate utility function, which includes both the monetary wealth and sentimental value as two arguments. We show that over (full, partial) insurance is optimal when a decrease in sentimental value will increase (not change, decrease, respectively) the marginal utility of monetary wealth. Moreover, a non-zero deductible exists even without administration costs. Furthermore, we demonstrate that a positive fixed reimbursement is optimal if (1) the premium is actuarially fair, (2) the monetary loss is a constant, and (3) the utility function is additively separable and the marginal utility of money is higher in the loss state than in the no-loss state. We also characterize comparative statics of fixed-reimbursement insurance under an additively separable preference assumption. JEL Classification G22 · D86 The author acknowledge funding from National Science Council in Taiwan (NSC93-2416-H-130-020).     

An Analysis of the Demand for Earthquake Insurance

This research examines the decision to purchase earthquake insurance by analyzing data on earthquake insurance price and penetration in the New Madrid fault zone in Missouri. Earthquake risk is of concern to consumers, the insurance industry, industry regulators, and government agencies because of the potentially catastrophic nature of losses resulting from a major earthquake. Despite the significance of the earthquake peril, the recent literature does not contain estimates of the price and income elasticity of the demand for earthquake insurance. Our analysis indicates that homeowners acquire earthquake insurance because of risk considerations, at higher levels of risk the demand for earthquake insurance is higher, and the price of earthquake coverage does not provide incremental information in explaining the demand for earthquake coverage.     

代际转移与商业养老保险对老年收入的影响差异研究

构建混合利他动机和交换动机下的世代交叠模型,研究个人最优消费决策,测算商业养老保险与代际转移对老年收入水平的影响。结果发现：代际转移支付比例提高会减少商业养老保险的购买,进而降低老年收入水平,与其他因素相比,保险价格变动对保险需求的影响最明显。鉴于此,应丰富居民投资结构,建设高质量的教育体系,发挥家庭养老除代际转移支付之外的多样化功能,同时通过供给侧降费推动居民参与商业养老保险。     

Overcoming Barriers to Life Insurance Coverage: A Behavioral Approach

While life insurance purchase decisions have long been studied, we still do not know how people decide if they need insurance or how much they need. Using in‐depth interviews, we peer into the black box of employee decision making to learn what people know about this employee benefit, and how they decide if it is of value for them. We find that individuals understand the need for life insurance, but find many behavioral economic barriers to getting adequate coverage, including mental accounting, money illusion, and a strong role of defaults. We then conduct an online experiment of the hypothetical employee‐benefit purchase scenario, and find a few, simple interventions could help individuals better decide their life insurance needs.     

Corporate capital structure and pension-funding strategy

This article provides an integrated analysis of pension funding and corporate financing strategies in the presence of default risk. The article shows that when the marginal personal income tax rate is constant, the financing decision with respect to pension funding is influenced entirely by tax considerations. When the marginal personal income tax is progressive, the optimal financing of pension funding depends on the cyclical nature of the firm (as characterized by the sign of beta), the riskiness of pension assets, and ERISA regulations concerning the pension-benefit guaranty rate, the marginal pension insurance premium and the firm's legal responsibility for its unfunded pension obligations. It is shown that a necessary condition for partial pension funding is that the marginal insurance premium imposed by PBGC must be less than actuarially fair, and a necessary condition for pension funding to be financed by both debt and equity is that beta must be positive.     

保险会计准则国际趋同：进展、困境与对策

通过对保险会计准则国际趋同进展与困境分析,可以发现：保险会计准则国际趋同进程中存在着分红保险一股独大、公允价值有关公允,会计信息可比性降低、保险监管指标计量基础改变等问题,鉴此,应改进保费收入的度量标准,完善准备金计量中有关折现率、风险调整和合同服务边际的评估标准,引入综合收益表列报方式,完善保险监管会计体系,强化监管要求。     

ON THE SHAREHOLDER WEALTH EFFECTS OF DEPOSIT INSURANCE PREMIUM REVISIONS ON LARGE,PUBLICLY TRADED COMMERCIAL BANKS

Evidence is provided from changes in deposit insurance premiums in the early 1990s on the validity of the premium absorption hypothesis and the premium shifting hypothesis. Analysis of abnormal market returns associated with deposit insurance events using a market‐model event‐study methodology suggests that reductions in deposit insurance premiums are associated with increases in the market value of banking organizations; conversely, increases in deposit insurance premiums are associated with decreases in market wealth. The largest banks in the sample and banks with low equity capital (and low risk‐based capital ratios) appear to be most affected. These results are generally consistent with the premium absorption hypothesis but inconsistent with the premium shifting hypothesis.