Richard D. MacMinn

Insurance and Corporate Risk Management

This paper provides a model of a competitive financial market economy in which there are not only stock and bond markets but also insurance markets. In the models most naive form, the analysis shows that the corporate value of the insured firm equals that of the uninsured firm and in this case the firm has no active role to assume in managing corporate risk. The model is then modified to incorporate costly bankruptcy and agency problems. Then the analysis shows that the corporation has an incentive to purchase insurance because it may eliminate or reduce the bankruptcy and/or agency costs.

THE UNDERINVESTMENT PROBLEM, BOND COVENANTS AND INSURANCE

This article complements the earlier work by Mayers and Smith (1987) and Schnabel and Roumi (1989) which showed that a property insurance contract could be used to bond subsequent corporate investment decisions. Although these models suggest one possible approach to solving the underinvestment problem, neither model explicitly specifies the economic mechanism(s) required to guarantee that current shareholders receive the maximum possible benefits from solving this problem. We propose a financing-constrained model that not only eliminates underinvestment but also ensures that current shareholders capture the entire agency cost (net of loading) as an increase in value.

Longevity/Mortality Risk Modeling and Securities Pricing

Securitization of longevity/mortality risk provides insurers and pension funds an effective, low-cost approach to transferring the longevity/mortality risk from their balance sheets to capital markets. The modeling and forecasting of the mortality rate is the key point in pricing mortality-linked securities that facilitates the emergence of liquid markets. The catastrophic longevity jumps and mortality jumps are significant in historical data and have a critical effect on securities pricing. This paper introduces a stochastic diffusion model with a Double Exponential Jump Diffusion (DEJD) process for mortality time-series, which is the first to capture both asymmetric jump features and cohort effect as the underlying reason for the mortality trend. The DEJD model has the advantage of easy calibration and mathematical tractability. The form of the DEJD model is neat, concise and practical. Compared with previous stochastic models with or without jumps, the DEJD model fits the actual data better. To apply the model, the implied risk premium is calculated based on the Swiss Re mortality bond price. The DEJD model is the first to provide a close-form solution to price the q-forward, which is the standard product contingent on the LifeMetrics index for hedging longevity or mortality risk.

Great (and not so great) expectations: An endogenous economic explication of insurance cycles and liability crises

ABSTRACT The causes of insurance cycles and liability crises have been vigorously sought, claimed, and debated by academic investigators for years. The model provided here partially synthesizes several stands of this literature and provides an additional cause. In addition to causes such as the loss-shocks and interest-rate changes included as explanations in the literature, this model posits changing expectations about the parameters of corporate net income as causes of cycles and crises. Since both sides of the market form expectations about losses and interest rates, changes in both demand and supply in the market are incorporated in the explanation. Changing expectations during the crisis reduced supply and made it more inelastic. The same changing expectations increased demand and made it more inelastic and so amplified the effect due to a change in supply. The model predicts an increase in the equilibrium premium, when the mean and variance of losses increase. The model also predicts an increase in the equilibri um premium when the mean interest rate decreases and variance increases. The empirical results of cross-sectional regression and time-series analyses are consistent with the predictions. The analysis then provides some insight on how to dampen future cycles and reduce the effect of future liability crises. INTRODUCTION Insurance cycles [2] have been recognized for decades and have been the object of study by academic investigators for that long (see Cummins, 1987). The reason for this intense study is both basic (theoretical) and practical. At a basic level, questions arise about whether such cycles conflict with rational corporate decision making in an efficient financial market. From a practical perspective, such cycles can, at their extreme-most valleys, create crises in affordability and availability of insurance, affecting the very productivity of the country involved. The liability insurance crisis in the United States from late 1984 through 1986 is an example of such an extreme in the insurance cycle, being characterized by significant economic disruptions in commercial liability insurance markets. The disruptions created concerns about both the availability and affordability of certain covers. For example, professional and commercial liability insurance consumers were adversely affected by the crisis, as were others such as chemical and pharmaceutical companies, day-care centers, doctors, and municipalities. The cycle ultimately resulting in the crisis was characterized by a sudden increase in liability premiums in late 1984 after about six years of relatively stable prices. An additional response to changes in this cycle included the lowering of policy limits and a reduction in scope of coverage in commercial liability lines that were characterized by long-tails. In addition, insurers were unwilling to provide any coverage at all for some risks, e.g., those involving pollution liability exposures. [3] Academics, attorneys general, consumers, insurers, and regulators have not agreed on the causes of insurance cycles, and the causes of the commercial liability insurance crisis of the late 1980s are still debated. The cycles and crisis theories that do appear in the literature share at least two common characteristics. First, the theories focus on the supply of liability insurance and ignore the demand. Although it is implicit in some theories, the demand for liability insurance during the cycles and crisis is generally not addressed. Second, the theories emphasize a single factor as the cause of the crisis or cycle, although exactly what the single factor is has varied from explanation to explanation. This shared single-factor approach to insurance cycle and crisis explications creates problems. First, the single-factor theories do not explain enough aspects of the crisis, even though each offers some insight. For example, the U. S. Justice Department (Justice, 1986) has cited the expansion of business liability under tort law as the factor explaining higher premiums and reduced coverage limits. …

Mossin's Theorem Given Random Initial Wealth

The purpose of this article is to reexamine Mossins Theorem under random initial wealth. Conditions necessary and sufficient for Mossins Theorem depend on the stochastic dependence between risks. The correlation coefficient, however, is not an adequate measure of stochastic dependence in the general expected-utility model, and so other notions of dependence are used to investigate Mossins Theorem. The inadequacy of the correlation coefficient is illustrated with two counterexamples. Then, using notions of positive and negative dependence measures, we provide necessary and sufficient conditions for a generalized Mossin Theorem to hold. In addition, a generalized Mossin Theorem is interpreted using the notion of a mean preserving spread made popular by Rothschild and Stiglitz (1970). Given a fair premium and dependent stochastic conditions, we show that an individual can obtain a final wealth distribution with less weight in its tails by selecting less than or more than full insurance.

On Corporate Insurance

Although insurance contracts are regularly purchased by corporations and play an important role in the management of corporate risk, only recently has this role received much attention in the finance literature. This paper provides a formal analytic survey of recent theoretical developments in the corporate demand for insurance. Insurance contracts are characterized as simply another type of financial contract in the nexus of contracts that comprise the corporation. The model developed here focuses specifically on the efficiency gains that can be derived from using corporate insurance contracts to reduce bankruptcy costs, agency costs, and tax costs.

Genetic Testing, Insurance Economics, and Societal Responsibility

Abstract Three major perspectives emerge when the discussion of the implications of genetic testing on the insurance industry commences. One viewpoint, strongly advocated by certain consumer groups and ethicists on the basis of societal responsibility, categorically denies any necessity for connecting the results of genetic testing and issuance of insurance. By contrast, the insurance industry, upon examining the economics and dynamics of participation in voluntary insurance markets, lives in fear of a world filled with asymmetrical information (counter to the axioms for competitive markets), adverse selection (action by the insured as a result of asymmetric information to the perceived economic disadvantage of the insurer), and ultimately even the possibility of potential market failure or insurance company insolvency. An actuarial perspective considering the benefits (to the insurer) of this new genetic information concentrates primarily on the possibility of developing improved quantitative assessments...

Longevity Risk and Capital Markets: The 2012–2013 Update

This Special Issue of the North American Actuarial Journal contains 15 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the articles were presented at Longevity Eight: The Eighth International Longevity Risk and Capital Markets Solutions Conference, which was held in Waterloo, Ontario, Canada, on September 7–8, 2012. It was hosted by the Department of Statistics and Actuarial Science at the University of Waterloo, Waterloo Research Institute in Insurance, Securities and Quantitative Finance (WatRISQ), and the Pensions Institute. It was sponsored by Prudential Financial, Inc., Sun Life Financial of Canada, Société Générale Corporate and Investment Banking, the Society of Actuaries (SOA), and the Canadian Institute of Actuaries (CIA). Longevity risk and related capital market solutions have grown increasingly important in recent years, both in academic research and in the markets we refer to as the new Life Market, that is, the capital market that trades longevity-linked assets and liabilities.1 Mortality improvements around the world are putting more and more pressure on governments, pension funds, and life insurance companies as well as individuals to deal with the longevity risk they face. At the same time, capital markets can, in principle, provide vehicles to hedge longevity risk effectively and transfer the risk from those unwilling or unable to handle it to those willing to invest in such risk in exchange for appropriate risk-adjusted returns or who have a counterpoising risk that longevity risk can hedge, such as life offices with mortality risk on their books. Many new investment products have been created both by the insurance/reinsurance industry and by the capital markets. Mortality catastrophe bonds are an example of a successful insurancelinked security. Some new innovative capital market solutions for transferring longevity risk include longevity (or survivor) bonds, longevity (or survivor) swaps, and mortality (or q-) forward contracts. The aim of the International Longevity Risk and Capital Markets Solutions Conferences is to bring together academics and practitioners from all over the world to discuss and analyze these exciting new developments. The conferences have followed closely the developments in the market. The first conference (Longevity One) was held at Cass Business School in London in February 2005. This conference was prompted by the announcement of the Swiss Re mortality catastrophe bond in December 2003 and the European Investment Bank/BNP Paribas/PartnerRe longevity bond in November 2004. The second conference was held in April 2006 in Chicago and hosted by the Katie School at Illinois State University.2 Since Longevity One, there have been further issues of mortality catastrophe bonds, as well as the release of the Credit Suisse Longevity Index. In the United Kingdom, new life companies backed by global investment banks and private equity firms were setting up for the express purpose of buying out the defined benefit pension liabilities of U.K. corporations. Goldman Sachs announced it was setting up such a buyout company itself (Rothesay Life) because the issue of pension liabilities was beginning to impede its mergers and acquisitions activities. It decided that the best way of dealing with pension liabilities was to remove them altogether from the balance sheets of takeover targets. So there was now firm evidence that a new global market in longevity risk transference had been established. However, as with many other economic activities, not all progress follows a smooth path. The EIB/BNP/PartnerRe longevity bond did not attract sufficient investor interest and was withdrawn in late 2005. A great deal, however, was learned from this failed issue about the conditions and requirements needed to launch a successful capital market instrument.

Corporate spin-offs as a value enhancing technique when faced with legal liability

Abstract The formation of spin-off companies by corporations facing unlimited liability exposures (e.g., oil spill liability by oil transport and oil production firms) is shown mathematically to actually increase shareholder wealth and firm value. This increase occurs at the expense of the liability claimants who essentially must absorb the cost of a put option on the value of the limited liability feature obtained by spinning off the company (a stop-loss type insurance premium). In addition to discussing this issue, the paper provides illustrations from current pollution liability history and considers differences between the stockholder/bondholder incentive conflicts and the stockholder/ liability claimant conflicts.

Incorporating Longevity Risk and Medical Information Into Life Settlement Pricing

A life settlement is a financial transaction in which the owner of a life insurance policy sells his or her policy to a third party. We present an overview of the life settlement market, exhibit its susceptibility to longevity risk, and discuss it as part of a new asset class of longevity‐related securities. We discuss pricing where the investor has updated information concerning the expected life expectancy of the insured as well as perhaps other medical information obtained from a medical underwriter. We show how to incorporate this information into the investors valuation in a rigorous and statistically justified manner. To incorporate medical information, we apply statistical information theory to adjust an appropriate prespecified standard mortality table so as to obtain a new mortality table that exactly reflects the known medical information. We illustrate using several mortality tables including a new extension of the Lee–Carter model that allows for jumps in mortality and longevity over time. The information theoretically adjusted mortality table has a distribution consistent with the underwriters projected life expectancy or other medical underwriter information and is as indistinguishable as possible from the prespecified mortality model. An analysis using several different potential standard tables and medical information sets illustrates the robustness and versatility of the method.