Abstract: Journal of Risk and InsuranceVolume 69, Issue 1 p. 45-62 Insurance Contracts and Securitization Neil A. Doherty, Neil A. DohertySearch for more papers by this authorHarris Schlesinger, Harris SchlesingerSearch for more papers by this author Neil A. Doherty, Neil A. DohertySearch for more papers by this authorHarris Schlesinger, Harris SchlesingerSearch for more papers by this author First published: 22 May 2002 https://doi.org/10.1111/1539-6975.00004Citations: 25 Neil Doherty and Harris Schlesinger work at the University of Pennsylvania and the University of Alabama, respectively. The authors thank seminar participants at the Universities of Konstanz, Munich, and Toulouse as well as at Tulane University for helpful comments on an earlier version of this article. Comments from Henri Loubergé and from three anonymous reviewers were especially helpful. See, for example, Cummins, Doherty, and Lo (2001) and Froot (2001). Basis risk need not be all bad. It may, for example, help to alleviate moral hazard problems. However, such issues go beyond the scope of this article. See Doherty (1997) for further discussion. See, for example, Borch (1962), Marshall (1974), Smith and Stultzer (1990), and Dionne and Doherty (1993). Although securitization may also affect markets through reductions in transaction costs (including agency costs), as compared to traditional insurance products, this is not a focus of the current article. Instead, the authors focus on the value of securitization aside from any effects upon transaction costs. Since transaction costs associated with insurance have often run on the order of 30 percent of premiums, the authors do not mean to imply that securitized products cannot have a large effect on cost efficiency. See, for example, Niehaus and Mann (1992) and Froot (2001). See Machina (1995), Karni (1995), and Schlesinger (1997) for summaries of insurance results in these models. The authors make this last assumption to avoid complications of modeling limited liability. The authors also wish to discourage thinking of ɛ as a loss amount itself. It is simply an adjustment to the long-run average loss that is experienced within a given year. Doherty and Schlesinger (1983) prove this result for a model using differentiable expected utility. Since full coverage for any treatment of ɛ is optimal for all risk averters defined via expected utility, it follows from Zilcha and Chew (1990, Theorem 1) that such behavior is optimal for the broader class of risk-averse preferences examined here. The result still holds if the utility function is not differentiable everywhere, which follows from Segal and Spivak (1990). If many pools of insureds exist, each with an ɛ that is independent of other groups', then γ possibly equals zero. The authors assume that a larger market does not exist to ``pass off'' the ɛ risk, so that γ>0. The authors also do not consider a general equilibrium model, in which the existence of the types of contracts proposed in this article have an effect on market prices, including a type of feedback effect upon γ itself. These conclusions follow easily along the lines suggested in note 7. Note that in Equation (1) only one source of uncertainty exists—ɛ . Note also that risk aversion is of order 1 if where the limit is taken over positive values of t, x is a zero-mean random variable, π(tx) is the risk premium such that −π(tx)?tx, and π′(tx) denotes ?π(tx)/?t for t>0. Risk aversion is of order 2 if π′(0x)=0 but π′′(0x)≠0. See Segal and Spivak (1990). More realistically, one would need to be concerned with the timing of premium collections and indemnity payouts. However, the authors abstract from these nuances in the static model. The total premium as given above is random ex ante. The premium actually paid ex post is dependent on the realized value of ɛ . One can think of the individual paying an up-front premium of αEL. The individual is then assessed an extra premium of αɛ . In the case where ɛ<0, this ``assessment'' is paid to the individual as a dividend. A negative modal value of ɛ would thus correspond to the payment of a dividend in most years under participating policies. Of course, the individual may be able to self-construct an equivalent contract via the purchase of two separate contracts, one fixed-premium contract with coverage level βα and one fully participating contract with coverage level 1−βα . This follows as in note 7. A sketch of the model in this section appears in Schlesinger (1999), who used it to examine losses from natural catastrophes. Since all choices of α leave the mean of H(α) and thus of Y in Equation (8) unchanged, second-order stochastic dominance follows from Rothschild and Stiglitz (1970, Theorem 2), since one can write where Of course, as n gets larger, so does the variance of total losses. This would lead to a higher bankruptcy risk absent any increase in insurer capital. Assume to circumvent this issue. See Doherty (1991) for a more complete discussion of the many complicated effects involved. Also, see item ``Insurance for Natural Catastrophes'' ahead for a discussion on how one might model correlated likelihoods. In a related article, Schlesinger (1999) provided some details of modeling loss severity correlations. He also provided a few numerical examples for interested readers. An extension by Loubergé and Schlesinger (2000) examined the interaction of severity correlation and frequency correlation. The authors provide the frequency risk analysis herein as a building block for these models as well as for future research. See Schlesinger (1999) for further discussion of the details of this case. Recently, new catastrophe indexes from Property Claims Services (PCS) have been added to those already in use (which uses data from the Insurance Services Office) to extend the product line offered by the CBOT. Obviously, the CBOT agrees with this assessment, that securitization is still developing in the marketplace. Moreover, other exchanges are coming into existence. For example, the newly opened Bermuda Commodities Exchange (BCOE) trades options contracts on certain ``atmospheric perils,'' such as tornadoes, hurricanes, and hailstorms, for specified regions within the United States. The contracts are based on a new index developed by a subsidiary of Guy Carpenter, and bidding takes place over the Internet. See Embrechts, Klüppelberg, and Mikosch (1997) for an excellent analysis of the multitude of problems involved in modeling long tails with extreme values. Another limitation in this model for dealing with extreme values is that the authors use the simplicity of proportional coverages, rather than the types of stop-loss contracts typically associated with such skewed distributions. This is the main focus of a recent article by Froot (2001). Although the damages were high, the amount of damages insured was only approximately $3 billion, according to data from Munich Reinsurance (see http://www.munichre.de). Munich Reinsurance also predicts that the maximum damage from a single California earthquake could be as high as $150 billion. Numbers are based on projections by the New York State Insurance Department and the Insurance Industry, respectively, as reported in the New York Post, January 15, 2002. 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