Significant attention has focused on the determinants of corporate insurance purchases. While this analysis generally involves observable firm characteristics, its implications have been untested. This is primarily due to the difficulty in obtaining data on corporate insurance purchases. The authors examine one industry where data on insurance purchases are systematically reported: the insurance industry. A reinsurance contract is an insurance policy purchased by one insurance company from another. Their examination of reinsurance purchases by property/casualty insurance companies provides strong evidence on the effects of ownership structure, size, geographic concentration, and line-of-business concentration on the demand for reinsurance. Copyright 1990 by the University of Chicago.

On the Corporate Demand for Insurance: Evidence from the Reinsurance Market

This article takes a contingent claim approach to the market valuation of equity and liabilities in life insurance companies. A model is presented that explicitly takes into account the following: (i) the holders of life insurance contracts (LICs) have the first claim on the company's assets, whereas equity holders have limited liability; (ii) interest rate guarantees are common elements of LICs; and (iii) LICs according to the so-called contribution principle are entitled to receive a fair share of any investment surplus. Furthermore, a regulatory mechanism in the form of an intervention rule is built into the model. This mechanism is shown to significantly reduce the insolvency risk of the issued contracts, and it implies that the various claims on the company's assets become more exotic and obtain barrier option properties. Closed valuation formulas are nevertheless derived. Finally, some representative numerical examples illustrate how the model can be used to establish the set of initially fair contracts and to determine the market values of contracts after their inception. INTRODUCTION The subject of fair valuation of life insurance liabilities has attracted a lot of attention in the insurance and finance literature in recent years. This is caused by the product structure of the life insurance business as well as certain events in the financial markets. The late 1980s through the 1990s was a period of quite some turmoil for the life insurance business, and Europe, Japan, and the United States can all present their own spectacularly long lists of defaulted life insurance companies. Many of these were relatively small, but some massive defaults of large economic significance also occurred including the United States' First Executive Corporation ($19 billion in assets), France's Garantie Mutuelle des Functionnaires (see Briys and de Varenne, 1994), and Nissan Mutual Life of Japan, which went bankrupt with uncovered liabilities of $2.56 billion (see Grosen and Jorgensen, 2000). In retrospective discussions of the reasons for these unfortunate events, three issues appear repeatedly. The first is the mismanagement of the interest rate guarantees issued with most life insurance policies. The second is the mismanagement of credit risk stemming from either side of the balance sheet, and the third relates to the application of poor or inappropriate accounting principles, which in many cases have critically delayed or suppressed potentially useful warning signs in relation to company solvency. These issues are, of course, closely interrelated, as will be further clarified in the subsequent discussion. The focus on the interest rate guarantee relates to the fact that most policies contain an explicit guarantee that the holder's account will be credited--on a year-to-year basis--with a rate of return (the policy interest rate) of at least some fixed guaranteed rate, say, 5 percent. At the time of issuance, the guaranteed interest rate has typically been (much) lower than prevailing market interest rates, a fact that has led companies to ignore their value (as well as their risk), and, to the best of the authors' knowledge, premiums for these issued guarantees (read: liabilities) have not been demanded anywhere before 1999. (1) However, as a result of a period when market interest rates have generally been declining and when guaranteed interest rates have been held fixed, the companies have experienced a dramatic narrowing in the safety margin between the earning power of their assets and the claims from issued liabilities. This particular development is a major source of the problems of some life insurance c ompanies, although it is also a bit ironic, because the fundamental function of insurance companies in general is to provide a guaranty of asset value to the customer, as pointed out by, e.g., Merton and Bodie (1992). Interest rate guarantees are thus a source of credit risk arising from the liability side of the balance sheet. …

Life Insurance Liabilities at Market Value: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework

This article considers a decentralized supply chain in which a single manufacturer is selling a perishable product to a single retailer facing uncertain demand. It differs from traditional supply chain contract models in two ways. First, while traditional supply chain models are based on risk neutrality, this article takes the viewpoint of behavioral principal‐agency theory and assumes the manufacturer is risk neutral and the retailer is loss averse. Second, while gain/loss (GL) sharing is common in practice, there is a lack of analysis of GL-sharing contracts in the supply chain contract literature. This article investigates the role of a GL-sharing provision for mitigating the loss-aversion effect, which drives down the retailer order quantity and total supply chain profit. We analyze contracts that include GL-sharing-and-buyback (GLB) credit provisions as well as the special cases of GL contracts and buyback contracts. Our analytical and numerical results lend insight into how a manufacturer can design a contract to improve total supply chain, manufacturer, and retailer performance. In particular, we show that there exists a special class of distribution-free GLB contracts that can coordinate the supply chain and arbitrarily allocate the expected supply chain profit between the manufacturer and retailer; in contrast with other contracts, the parameter values for contracts in this class do not depend on the probability distribution of market demand. This feature is meaningful in practice because (i) the probability distribution of demand faced by a retailer is typically unknown by the manufacturer and (ii) a manufacturer can offer the same contract to multiple noncompeting retailers that differ by demand distribution and still coordinate the supply chains.

Channel Coordination for a Supply Chain with a Risk‐Neutral Manufacturer and a Loss‐Averse Retailer*

In this article we deal with the problem of pricing a guaranteed life insurance participating policy, sold in the Italian market, which embeds a surrender option. This feature is an American-style put option that enables the policyholder to sell back the contract to the insurer at the cash surrender value. Employing a recursive binomial formula patterned after the Cox, Ross, and Rubinstein (1979) discrete option pricing model we compute, first of all, the total price of the contract, which also includes a compensation for the participation feature ("participation option," henceforth). Then this price is split into the value of three components: the basic contract, the participation option, and the surrender option. The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice.

Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option

A theoretical model is developed in which the supply and demand for life assurance is determined by various economic and social variables. The implications of this model for the determination of premium income are investigated empirically by pooling cross-section and time-series data for ten industrialised countries over the period 1970–1981. We find that life assurance premiums vary directly with life expectancy, the age distribution of the population, the dependency ratio, interest rates and income, but vary inversely with social security coverage. Our results indicate the importance of distinguishing between single and regular premiums but our data prevent us from taking this adequately into account.

The determination of life premiums: An international cross-section analysis 1970–1981

A typical life insurance contract provides a package of options or rights to the policyowner that is not precisely duplicated by any other combination of commonly available contracts. Viewed from this perspective, life insurance enjoys a unique position in the field of investments and should be judged in this light. The paper shows that an options viewpoint provides a more complete explanation of policyowner behavior towards life insurance than the conventional savings-andprotection view. Also, the paper examines the effect of the options viewpoint in restating the amount of insurance protection and discusses implications of the options view for product development and cost disclosure. The persistence of whole life insurance in the United States during the last decade is somewhat a mystery if the product is regarded as a simple package of savings and term insurance. Yields offered by competing investments generally were higher than returns on life insurance cash values, so the failure of many policyholders to surrender their contracts in favor of higher yielding investments is puzzling. Tax advantages of whole life insurance provide a partial explanation, but other investments dominate life insurance if yield and tax advantages are considered together. Municipal bonds have provided similar tax advantages with a higher average yield' while an Individual Retirement Account or a Keogh Plan has offered greater tax advantages with a similar yield.2 Why does whole life insurance continue to exist? This-paper answers this question by offering a new perspective on whole life insurance and other life insurance products. It demonstrates that a life insurance contract is a package

The Life Insurance Policy as an Options Package

Retroactive liability insurance may be written to provide coverage for a known loss that occurred during a past time period. Some simplified financial models are developed in this paper in order to provide some economic insights about the market for this coverage. The financial motives and conditions for the development of this market are analyzed. In particular, federal income taxes provide economic incentives for writing the coverage. Tax arbitrage enables the insured to share the income tax deductions for loss reserves available to an insurer when the coverage is written. Interest rates, insurer expenses. and the expected time to settlement influence the development of the market. Potential incentive conflicts may arise, however.

An Economic Analysis of Retroactive Liability Insurance

Properly pricing deductible may help insurers to meet business objectives such as minimizing adverse selection, eliminating small claims, maintaining risk charges, and minimizing policyowner dissatisfaction. Technical considerations-such as the nature of loss data, the effect of inflation, and the effect of deductibles on operating costs-impose constraints on pricing procedures. After analyzing these business objectives and technical considerations, this paper concludes that a deductible pricing decision may involve compromises among competing requirements and objectives. Furthermore, some of the accepted wisdom of deductibles-such as their effect in reducing "nuisance claims"-is opened to serious question. Although an insurer's problem of setting rate credits for deductibles is at least as complex and worthy of study as the insurance buyer's problem of selecting a deductible, the insurance seller's decision has not received the intensive analysis long focused on the buyer's problem. This paper seeks partially to correct this imbalance by setting forth guidelines insurers may follow rationally in pricing deductibles for property insurance coverages. Pricing guidelines emanate from two sources: an insurer's business objectives and technical considerations which underlie proper rate credits. To meet its business objectives, one of which presumably is an underwriting profit, an insurer should offer deductibles and set deductible credits which,

http://www.jstor.org/stable/pdfplus/251673.pdf

Guidelines for Insurers in Pricing Deductibles

The Pricing and Marketing of Insurance

A policyowner who wishes to select a deductible faces a problem in decision making under uncertainty. A question that the policyowner needs to answer is whether s/he is willing to assume the risk of possible large uncovered losses in return for the premium savings associated with a larger deductible. Proposed in this article is a method for applying risk-return analysis to deductible selection problems. A theoretical approach to selecting optimum deductibles is developed in this article. The approach consists of analyzing both risk and expected cost to select an optimum deductible amount. The method proposed is similar to a type of risk-return analysis used as a corner-stone of financial theory. Limitations of the method are noted and distinguishing characteristics of deductible selection problems are outlined.

http://www.jstor.org/stable/pdfplus/251908.pdf

Applying Risk-Return Analysis to Deductible Selection Problems: A Mathematical Approach

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