Consumer risk perceptions and information in insurance markets with adverse selection

Standard models of adverse selection in insurance markets assume policyholders know their loss distributions. This study examines the nature of equilibrium and the equilibrium value of information in competitive insurance markets where consumers lack complete information regarding their loss probabilities. We show that additional private information is privately and socially valuable. When the equilibrium policies separate types, policyholders can deduce the underlying probabilities from the contracts, so it is information on risk type, rather than loss probability per se, that is valuable. We show that the equilibrium is “as if” policyholders were endowed with complete knowledge if, and only if, information is noiseless and costless. If information is noisy, the equilibrium depends on policyholders' prior beliefs and the amount of noise in the information they acquire.     

Pricing the risks of default

This paper decomposes default risk into timing and recovery risks. The two default components are explicitly priced as if they were traded in the futures market. We develop estimation strategies evaluating recovery risks and then construct implicit prices of contingent securities reflecting purely the timing risk. The models are estimated on monthly data for rates on certificates of deposit offered by institutions in the Savings and Loan Industry, during the 1987–1991 period. Empirical results support market expectations of lower likelihoods of default after 1989.     

A Complete Analysis of Full Pareto Efficiency in Financial Markets for Arbitrary Preferences

This paper provides a complete analysis of the necessary and sufficient conditions for financial markets to achieve fully Pareto-efficient allocation of aggregate wealth through trade in economies with arbitrary preferences. We show that full Pareto efficiency obtains only if the market structure of contingent claims spans the information partition of a minimal aggregate wealth statistic and a Halmos-Savage sufficient statistic for the beliefs of the traders. All the known allocation efficiency results in the literature due to Arrow, Hakansson, John, Ross, and others are unified by this result.     

Financial Intermediaries, Markets, and Growth

We build a model in which financial intermediaries provide insurance to households against idiosyncratic liquidity shocks. Households can invest in financial markets directly if they pay a cost. In equilibrium, the ability of intermediaries to share risk is constrained by the market. From a growth perspective, this can be beneficial because intermediaries invest less in the productive technology when they provide more risk-sharing. Our model predicts that bank-oriented economies can grow more slowly than more market-oriented economies, which is consistent with some recent empirical evidence.     

Social Security with Heterogeneous Populations Subject to Demographic Shocks

In a previous paper, we showed how a pay-as-you-go social security scheme, based on voluntary contributions, can be an appropriate institution to reach an optimal sharing of risks among generations in the presence of demographic uncertainties. We study here the functioning of such schemes when there are different population strata, with different demographic shocks and wages. We show that while a collective voluntary pay-as-you-go scheme can provide efficient intergenerational risk sharing, it is likely to be destabilized by pensions funds specialized by agents' types. This is true both when there is a complete set of contingent markets, where the risk pooling capabilities of a collective fund are potentially of less interest, and when markets are incomplete. In this last circumstance, a collective fund may help the living agents to share their intragenerational risks. However, we show that the resulting allocation does not Pareto dominate the outcome of individual funds by agent types, and that there are incentives for agents to separate from any collective organization.     

Neglected risks,financial innovation,and financial fragility

We present a standard model of financial innovation, in which intermediaries engineer securities with cash flows that investors seek, but modify two assumptions. First, investors (and possibly intermediaries) neglect certain unlikely risks. Second, investors demand securities with safe cash flows. Financial intermediaries cater to these preferences and beliefs by engineering securities perceived to be safe but exposed to neglected risks. Because the risks are neglected, security issuance is excessive. As investors eventually recognize these risks, they fly back to the safety of traditional securities and markets become fragile, even without leverage, precisely because the volume of new claims is excessive.     

A general class of distortion operators for pricing contingent claims with applications to CAT bonds

ABSTRACT

The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the (Wang 2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g. skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.     

Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty

In diffusion models, a few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow–Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow–Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow–Debreu equilibrium allocations are generically unattainable by dynamically trading a few long-lived assets.     

The Probationary Period as a Screening Device: The Monopolistic Insurer

Stiglitz [1977], considering asymmetry of information in a monopolistic insurance market and the monetary deductible as a screening device, shows that an equilibrium is always of a separating type. High risks buy complete insurance whilst low risks buy partial insurance. In this paper, we show that a pooling equilibrium may exist if a probationary period, rather than the partial coverage in monetary terms, is used as a screening device.JEL Classification No.: D42, D82     

The Spillover effect of compulsory insurance

The assumption usually made in the insurance literature that risks are always insurable at the desired level does not hold in the real world: some risks are not—or are only partially—insurable, while others, such as civil liability or health and workers' injuries, must be fully insured or at least covered for a specific amount. We examine in this paper conditions under which a reduction in the constrained level of insurance for one risk increases the demand of insurance for another independent risk. We show that it is necessary to sign the fourth derivative of the utility function to obtain an unambiguous spillover effect. Three different sufficient conditions are derived if the expected value of the exogenous risk is zero. The first condition is that risk aversion be standard—that is, that absolute risk aversion and absolute prudence be decreasing. The second condition is that absolute risk aversion be decreasing and convex. The third condition is that both the third and the fourth derivatives of the utility function be negative. If the expected value of the exogenous risk is positive, a wealth effect is added to the picture, which goes in the opposite direction if absolute risk aversion is decreasing.     

Time Deductibles as Screening Devices: Competitive Markets

Seminal papers on asymmetric information in competitive insurance markets, analyzing the monetary deductible as a screening device, show that any existing equilibrium is of a separating type. High risks buy complete insurance, whereas low risks buy partial insurance—and this result holds for the Nash behavior as well as for the Wilson foresight. In this article, we analyze the strength of screening based on limitations to the period of coverage of the contract. We show that in this case (1) the Nash equilibrium may entail low risks not purchasing any insurance at all, and (2) under the Wilson foresight, a pooling equilibrium may exist.     

The Determinants of Financial Health of Asian Insurance Companies

Previous studies of financial health of insurance companies are mainly focused on insurers operating in the United States and developed economies. This article focuses on the solvency of general (property‐liability) and life insurance companies in Asia using firm data and macro data separately. It uses different classification methods to classify the financial status of both general and life insurance companies. With the exception of Japan, failures of insurers in Singapore, Malaysia, and Taiwan are nonexistent. We find that, first, the factors that significantly affect general insurers' financial health in Asian economies are firm size, investment performance, liquidity ratio, surplus growth, combined ratio, and operating margin. Second, the factors that significantly affect life insurers' financial health are firm size, change in asset mix, investment performance, and change in product mix, but the last three factors are more applicable to Japan. Third, the financial health of insurance companies in Singapore seems to be significantly weakened by the Asian Financial Crisis. As the insurance industry in different Asian economies is at different stages of development, they require different regulatory guidelines.     

Financial equilibrium with non-linear valuations

Classical Arrow Debreu equilibria employ budget feasibility to require individuals to ensure excess supplies to be nonnegative in value using the single equilibrium price system for valuation purposes. Yet by the selection of state contingent prices, they seek excess supplies that are nonnegative in each component, and not just the value. A financial equilibrium, on the other hand, defines acceptable economic risks as excess supplies that are nonnegative in value for a number of prespecified valuation price systems. The collection of prespecified valuation price systems may be referred to as features for which clearing is sought. The number of features will generally be less than the number of states. It is then shown that by also defining budget feasibility nonlinearly one may construct a financial equilibrium with fewer securities than there are features to be cleared.     

Equilibrium in risk-sharing games

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. In this paper, we propose a game where agents’ strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow–Debreu sharing rules. First, it is shown that agents’ best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation, and it is proved to exist for an arbitrary number of agents and to be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different from their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk-tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium than compared to the Arrow–Debreu one.     

银行监管和股东属性对银行风险的影响——基于新兴经济体的监管数据分析

银行监管按世界银行的标准划分为总体监管和12类分项监管;银行大股东属性包括政府类、金融企业类、外资类等.总体监管可以有效地降低银行风险;大股东为工业类、金融类企业的银行能够更好地控制风险,而家族类银行的风险程度较高;通过对分项监管进行研究可以发现,加强对所有权、资本要求、经营活动限制、外部审计要求、流动性、存款保险制度、退出及监管效率八个方面的监管可降低银行总体风险,而加强准入、内部管理、资产分类配置、信息披露这四类监管反而会增加银行总体风险.     

Stochastic dividend yields and derivatives pricing in complete markets

When an underlying yields a stochastic dividend yield, derivatives with linear payoff at their maturities that are written on this underlying have the following properties: (i) they have a unique price only if markets are complete; (ii) the dynamic strategies that replicate these contingent claims contain hedging components against the state variables in the economy; (iii) the prices of these derivatives will depend upon the dynamics of the market prices of risk even when markets are complete. Within an affine framework, we explicitly price forward and futures contracts with stochastic dividends. We also show that the quantitative impact of assuming that dividends are deterministic when they are actually stochastic is significant. JEL Classification G12 · G13     

A Value at Risk Approach to Background Risk

This paper studies the effects of an uninsurable background risk (BR) on the demand for insurance (proportional and with deductible). We study both the case of BR uncorrelated with the insurable one and the perfectly correlated one, in a Gaussian world. In order to perform our study, we exploit the new risk measure known as Value at Risk (VaR) and consider insurance contracts which are Mean-VaR efficient. We obtain results which depend on the parameters (moments) of both risks and on the magnitude of loadings charged by the insurance company, instead of depending on the risk attitudes of the insured, such as risk aversion and prudence.We demonstrate that, if loadings are not too high, the demand for insurance increases with positively correlated BR; it decreases with BR negatively correlated if the latter is less risky than the insurable one (in this case it can even go to zero, if loadings are too high); it goes to zero with BR which is negatively correlated and more risky than the insurable one.     

The Equilibrium Valuation of Risky Discrete Cash Flows in Continuous Time

This paper values a contingent claim to discrete stochastic cash flows generated by a Poisson arrival process with a randomly varying intensity parameter. In the most general case, both the size and the arrival intensity of cash flows may correlate wih state variables in a continuous time economy. Assuming the conditions of an intertemporal capital aset pricing model, solutions for the value of the contingent claim can be found using various techniques. The paper suggests immediate applications to the valuation of insurance contracts, the decision to build a firm with unknown future investment opportunities, and the pricing of mortgage-backed securities.     

Representation of concave distortions and applications

ABSTRACT

A family of concave distortion functions is a set of concave and increasing functions, mapping the unity interval onto itself. Distortion functions play an important role defining coherent risk measures. We prove that any family of distortion functions which fulfils a certain translation equation, can be represented by a distribution function. An application can be found in actuarial science: moment-based premium principles are easy to understand but in general are not monotone and cannot be used to compare the riskiness of different insurance contracts with each other. Our representation theorem makes it possible to compare two insurance risks with each other consistent with a moment-based premium principle by defining an appropriate coherent risk measure.     

Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization

Normalized exponential tilting is an extension of classical theories, including the Capital Asset Pricing Model (CAPM) and the Black–Merton–Scholes model, to price risks with general‐shaped distributions. The need for changing multivariate probability measures arises in pricing contingent claims on multiple underlying assets or liabilities. In this article, we apply it to valuation of mortality‐based securities written on mortality indices of several countries. We show how to use multivariate exponential tilting to price the first pure mortality security, the Swiss Re bond. The same technique can be applied in other mortality securitization pricing.