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Abstract:
Credit risk is pervasive throughout financial markets. Traditionally, various financial institutions have assumed the burden of credit risk. Banks have supported the credit risk attached to bank loans and forward contracts. Credit insurance companies have provided coverage for the commercial credit risk faced by suppliers of consumer and investment goods and services. Public insurers, such as the ECGD in the UK, have specialized in the coverage of credit risk attached to export trade and overseas investment. Specialized institutions, such as factoring companies, have offered credit risk coverage as one component in a basket of financial services. More recently, the proliferation of financial contracts that entail counter-party default risk - such as swaps, back-to-back loans, and derivative products - have focused attention on ways to deal with credit risk in the marketplace. New products, such as credit default swaps, credit spread options and total-rate-of-return swaps, have allowed firms and financial institutions to more effectively deal with credit risks. Indeed, a recent survey by the British Banker's Association estimates the current market for credit derivative to be around $900 billion in notional principal, with that amount expected to jump to over $1.5 trillion in 2002. In addition, insurance markets have reacted with an array of new products, many with the backing of larger capital markets, such as insurance-linked securities and finite-risk contracts (Shimpi 1999).

Abstract:
High correlations between risks can increase required insurer capital and/or reduce the availability of insurance. For such insurance lines, securitization is rapidly emerging as an alternative form of risk transfer. The ultimate success of securitization in replacing or complementing traditional insurance and reinsurance products depends on the ability of securitization to facilitate and/or be facilitated by insurance contracts. The authors consider how insured losses might be decomposed into separate components, one of which is a type of 'systemic risk' that is highly correlated among insureds. Such a correlated component might conceivably be hedged directly by individuals but is more likely to be hedged by the insurer. The authors examine how insurance contracts may be designed to allow the insured a mechanism to retain all or part of the systemic component. Examples are provided that illustrate this methodology in several types of insurance markets subject to systemic risk.

Abstract:
High correlations between risks can increase required insurer capital and/or reduce the availability of insurance. For such insurance lines, securitization is rapidly emerging as an alternative form of risk transfer. The ultimate success of securitization in replacing or complementing traditional insurance and reinsurance products depends on the ability of securitization to facilitate and/or be facilitated by insurance contracts. We consider how insured losses might be decomposed into separate components, one of which is a type of "systemic risk" that is highly correlated amongst insureds. Such a correlated component might conceivably be hedged directly by individuals, but is more likely to be hedged by the insurer. We examine how insurance contracts may be designed to allow the insured a mechanism to retain all or part of the systemic component. Examples are provided, which illustrate our methodology in several types of insurance markets subject to systemic risk.

Abstract:
We examine asset prices in a representative-agent model of general equilibrium. Assuming only that individuals are risk averse, we determine conditions on the changes in asset risk that are both necessary and sufficient for the asset price to fall. We show that these conditions neither imply, nor are implied by the conditions for second-degree stochastic dominance. For example, if the payoff on an asset becomes riskier in the sense of second-degree stochastic dominance, the equilibrium price of the asset need not necessarily fall. We further demonstrate how our results can be imbedded into a market that is incomplete in the sense of containing an uninsurable background risk, such as a risk on labor income. We extend our model to show how a miscalibration of the asset risk can lead to a partial explanation of high equity premia (i.e., the "equity premium puzzle").

Asset Pricing, Stochastic Dominance, Equity Premium Puzzle

Abstract:
This paper examines preferences towards particular classes of lottery pairs. We show how concepts such as prudence and temperance can be fully characterized by a preference relation over these lotteries. If preferences are defined in an expected-utility framework with differentiable utility, the direction of preference for a particular class of lottery pairs is equivalent to signing the nth derivative of the utility function. What makes our characterization appealing is its simplicity, which seems particularly amenable to experimentation.

properness, prudence, risk apportionment, risk aversion, stochastic dominance, temperance, utility premium

Abstract:
We consider a competitive insurance market with adverse selection. Unlike the standard models, we assume that individuals receive the benefit of some type of potential government assistance that guarantees them a minimum level of wealth. For example, this assistance might be some type of government-sponsored relief program, or it might simply be some type of limited liability afforded via bankruptcy laws. Government assistance is calculated ex post of any insurance benefits. This alters the individuals' demand for insurance coverage. In turn, this affects equilibria in various insurance models of markets with adverse selection.

adverse selection, insurance, government relief

Abstract:
Decisions under risk are often multidimensional, where the preferences of the decision maker depend on several attributes. For example, an individual might be concerned about both her level of wealth and the condition of her health. Many times the signs of successive cross derivatives of a utility function play an important role in these models. However, there has not been a simple and intuitive interpretation for the meaning of such derivatives. The purpose of this paper is to give such an interpretation. In particular, we provide an equivalence between the signs of these cross derivatives and individual preference within a particular class of simple lotteries.

correlation aversion, multivariate risk, prudence, risk aversion, temperance

Abstract:
We examine the effects of non-portfolio risks on optimal portfolio choice. Examples of non-portfolio risks include, among others, uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities. In particular, while some of these risks are added to portfolio value and have been amply studied, others are multiplicative in nature and have received far less attention. Moreover, the combined effects of multiple risks lead to some seemingly paradoxical choice behavior. We rationalize such behaviour and we show how non-portfolio risks might lead to seemingly U-shaped relative risk aversion for a representative investor, as found empirically by Ait-Sahilia and Lo (2000) and Jackwerth (2000).

Portfolio choice, Derived relative risk aversion, Additive background risk, Multiplicative background risk

Abstract:
Higher-order risk effects play an important role in examining economic behavior under uncertainty. A precautionary demand for saving has been linked to the property of prudence and the property of temperance has been used to show how the presence of an unavoidable risk affects one's behavior towards a second risk. These two properties also play key roles in aversion to negative skewness and to kurtosis, respectively. Both properties recently have been characterized by preferences over lottery pairs in simple 50-50 gambles. The simplicity of this characterization is ideal for experimental investigation. This paper reports the results of such experiments and concludes that there is behavioral evidence for prudence, but not for temperance. Implications of these results for both expected-utility and non-expected-utility models are examined.

risk, prudence, temperance, laboratory experiments

Abstract:
We examine how long-term life insurance contracts can be designed to incorporate uncertain future bequest needs. An individual who buys a life insurance contract early in life is often uncertain about the future financial needs of his or her family, in the event of an untimely death. Ideally, the individual would like to insure the risk of having high future bequest needs; but since bequest motives are typically unverifiable, a contract directly insuring these needs is not feasible. We derive two equivalent long-term life insurance contracts that are incentive compatible and achieve a higher welfare level than the naive strategy of delaying the purchase of insurance until after one's bequest needs are known. We also examine the welfare effects of such contracts and we show how third-party financial products, although beneficial to the individual in the short run, can be welfare decreasing over one's lifetime.

asymmetric information, bequest needs, life insurance

Abstract:
This paper characterizes higher order risk effects, such as prudence and temperance, via preferences that partially order a set of simple 50-50 lotteries.

Downside Risk, Precautionary Savings, Prudence, Risk Apportionment

Abstract:
How does risk affect saving? Empirical work typically examines the effects of detectible differences in risk within the data. How these differences affect saving in theoretical models depends on the metric one uses for risk. For labor-income risk, second-degree increases in risk require prudence to induce increased saving demand. However, prudence is not necessary for first-degree risk increases and not sufficient for higher-degree risk increases. For increases in interest rate risk, a precautionary effect and a substitution effect need to be compared. This paper provides necessary and sufficient conditions on preferences for an Nth-degree change in risk to increase saving.

precautionary saving, prudence, stochastic dominance, temperance

Abstract:
Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50-50 lottery [XN + YM, YN + XM] dominates the lottery [XN + XM, YN + YM] via (N + M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N + M)th-order stochastic dominance preference will allocate the state contingent lotteries in such a way as not to group the two bad lotteries in the same state, where bad is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher order risk effects, such as precautionary effects and tempering effects.

downside risk, precautionary effects, prudence, risk apportionment, risk aversion, stochastic dominance, temperance

Abstract:
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.

Abstract:
This article considers a zero-mean background risk that is uncorrelated with insurable losses, but is not necessarily statistically independent. In particular, the size of the background risk can vary in different insurable-loss states. We show how a prudent individual will buy either more insurance or less insurance than with no background risk, depending on the relative size of the background risk in the loss states vis-á-vis the no-loss states. If we consider two individuals, with one more risk averse than the other, we need to compare the intensities of their precautionary motives, in addition to their measures of risk aversion, before we can determine who buys more insurance coverage in the presence of the state dependent background risk.

Abstract:
We consider a competitive insurance market with adverse selection. Unlike the standard models, we assume that individuals receive the benefit of some type of potential government assistance that guarantees them a minimum level of wealth. For example, this assistance might be some type of government-sponsored relief program, or it might simply be some type of limited liability afforded via bankruptcy laws. Government assistance is calculated ex post of any insurance benefits. This alters the individuals' demand for insurance coverage. In turn, this affects the equilibria in various insurance models of markets with adverse selection.

Abstract:
This article shows how the introduction of severity risk into a simple model of insurance markets affects the optimal level of insurance. Also examined is how severity risk affects the equilibrium for an insurance market exhibiting adverse selection in the frequency risk. Individuals are assumed to possess identical loss severity distributions, but differ in their privately-known probabilities of having a loss. In particular, the effects of severity risk on the Nash equilibrium of Rothschild and Stiglitz (1976), on the anticipatory equilibrium of Wilson (1977), and on Miyazaki's (1977) extension of Wilson's equilibrium are analyzed. Severity risk is shown to affect the type of equilibrium contracts (pooling vs. separating), equilibrium levels of coverage, and overall societal welfare.

Abstract:
This article models consumption and insurance decisions in a continuous-time, finite-horizon setting. We allow the consumer to acquire a "taste for the good life" by making current preferences for consumption dependent upon the individual's past consumption. The optimal consumption path is smoother and the optimal level of insurance greater in this setting than they are in an identical model without habit formation. Moreover, the optimal level of insurance increases over the planning horizon, approaching full coverage in the limit. These results help to explain the observed phenomenon of individuals' over-purchasing insurance, such as a propensity for low deductibles.

Abstract:
This article focuses on two cornerstone results in insurance economics: Mossin's Theorem on the optimality of full versus partial coverage, and Arrow's Theorem on the optimality of straight deductible policies. Both of these results are examined in a model assuming only risk aversion, and not necessarily expected-utility maximization. The results also are examined with the inclusion of a noninsurable background risk. Arrow's result is robust enough to hold in all of these situations. Mossin's result is shown to hold with a slight weakening, to account for possible "nonsmoothness" of preferences in non-expected-utility models.