Abstract
The chapter reviews the evolution in insurance economics over the past 40 years, by first recalling the situation in 1973, then presenting the developments and new approaches which flourished since then. The chapter argues that these developments were only possible because steady advances were made in the economics of risk and uncertainty and in financial theory. Insurance economics has grown in importance to become a central theme in modern economics, providing not only practical examples to illustrate new theories, but also inspiring new ideas of relevance for the general economy.
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Notes
- 1.
Note that all chapters appearing in the 2000 version of this Handbook are excluded from the reference list, on the expectations that the present version includes revised version of these surveys.
- 2.
Note that two of these six authors, Kenneth Arrow and Gary Becker, received later the highest distinction for economic research—the Nobel Prize in economics.
- 3.
- 4.
Actually, Borch’s theorem was already present in Borch (1960), but the latter article was primarily written for actuaries, whereas the 1962 Econometrica article was addressed to economists.
- 5.
HARA = Hyperbolic Absolute Risk Aversion. As noted by Drèze (1990), the linearity of the sharing rule follows from the linearity of the absolute risk tolerance implied by hyperbolic absolute risk aversion.
- 6.
The question whether or not “institutions” are needed to allocate risks in the economy was tackled later in the finance literature.
- 7.
The applications of Borch’s theorem in the actuarial literature are reviewed by Lemaire (1990).
- 8.
More precisely, Schlesinger (1997) considers one version of Arrow’s theorem: the case where the insurer is risk neutral and the insured is risk averse (risk aversion being defined by Schlesinger as preferences consistent with second-degree stochastic dominance). In this case a straight deductible policy is optimal whenever the insurer’s costs are proportional to the indemnity payment.
- 9.
- 10.
Incomplete insurance may be obtained using a deductible or coinsurance (or both).
- 11.
The survey of developments presented in the next three sections draws on the excellent survey of insurance economics originally proposed by Dionne and Harrington (1992).
- 12.
Other strange results were observed later on, for example an increased loss probability has an ambiguous impact on insurance purchasing if the insured has DARA preferences and the insurer adjusts the premium to take the increased loss probability into account (Jang and Hadar 1995).
- 13.
It is obvious that the paradox may be resolved if one introduces differential information. If the insured overestimates the probability (or the amount) of loss, full insurance may be optimal, even when the premium is loaded with a fixed proportional factor.
- 14.
On a related theme, see also Doherty and Schlesinger (1990) for the case where the insurance contract itself is risky, due to a nonzero probability of insurer default. The article shows that full insurance is not optimal under fair insurance pricing, and that the usual comparative statics result from the single risk model do not carry over to the model with default risk. Their work was extended by Cummins and Mahul (2003) to the case where the insurer and policyholder have divergent beliefs about the insurer default risk.
- 15.
In a recent article, Hong et al. (2011) argue that correlation is not an adequate measure of stochastic dependence when expected utility is used. Turning to more general notions of positive and negative dependence, and focussing on coinsurance, they show that the individual will purchase less than full (more than full) insurance if and only if the insurable risk is positively (negatively) expectation dependent with random initial wealth.
- 16.
These theoretical advances closely followed similar advances in the theory of risk premiums under multiple sources of risk: Kihlstrom et al. (1981), Ross (1981), and Doherty et al. (1987). This literature on optimal insurance in presence of a background risk has also close links to the literature on the demand for a risky asset which was pioneered by Arrow (1963b) in a single risk setting and developed later to consider the impact of background risks: see, e.g., Tsetlin and Winkler (2005) and Li (2011) for recent contributions.
- 17.
This case corresponds to a negative cross-derivative of the two-attribute utility function (u 12 ≤ 0). Eeckhoudt et al. (2007) show that this is equivalent to “correlation aversion,” the aversion to losses affecting simultaneously the two attributes of utility (health and wealth for example).
- 18.
Following Eeckhoudt et al. (2007), the individual is then “correlation loving.” For him, in this case, purchasing more insurance against a loss in wealth helps to mitigate the adverse impact of a negative correlation between the two risks.
- 19.
The following developments on this topic borrow from the literature review in Loubergé and Watt (2008).
- 20.
Coinsurance must be excluded to avoid corner solutions of either no holding of the riskless asset or zero demand for insurance. Meyer and Meyer (1998b) address the specific case of deductible insurance.
- 21.
In this case, with increasing wealth, the rate of increase of the possible loss amount is higher than the rate of decrease of relative risk aversion.
- 22.
Using Mossin’s (1968) approach, Jang and Hadar (1995) obtain that the effect of an increase in the probability of loss is in this case indeterminate if the utility function displays DARA, and that the demand for insurance decreases with CARA or IARA utility.
- 23.
Jullien et al. (1999) showed later that “self-protection increases with risk aversion if and only if the initial probability of loss is low enough.”
- 24.
See also Courbage and Rey (2006) for an extension of this result to the case of two-argument utility functions, wealth, and health.
- 25.
The effect of wealth on self-protection expenses is null under CARA and it depends on the level of the loss probability under DARA and IARA.
- 26.
Note that all this literature on self-insurance and self-protection has been driving away from the study of the links between insurance demand and prevention. In addition, except for the recent article by Lee (2012), it has focussed on the case where prevention implies a monetary cost (prevention expenditures), instead of the case where prevention implies an “effort” producing a direct loss in utility—presumably because the analysis of the latter case is more straightforward.
- 27.
Under the negligence rule, an injurer cannot be made liable for the losses imposed on a victim if the injurer has applied the appropriate level of care. In theoretical work, the appropriate level of care is the socially efficient level of care optimally chosen by a risk averse potential injurer if the judgment proof problem does not arise. This level balances the marginal benefits and marginal cost of care.
- 28.
In addition, the injurer would run the risk of being denied indemnification by the insurer if it turned out ex post that the level of care was inappropriate.
- 29.
The orders of risk aversion, as defined by Segal and Spivak (1990), rest on the behavior of the risk premium in the limit, as the risk tends toward zero.
- 30.
This result is reminiscent of the same result obtained under Hurwicz’s model of choice under risk: see Briys and Loubergé (1985).
- 31.
An economic equilibrium is efficient if it is Pareto optimal: it is impossible to organize a reallocation of resources which would increase the satisfaction of one individual without hurting at least one other individual. The first theorem of welfare economics states that any competitive equilibrium is Pareto optimal, and the second theorem states that a particular Pareto optimum may be reached by combining lump sum transfers among agents with a competitive economic system. In an efficient equilibrium, market prices reflect social opportunity costs.
- 32.
In an interesting article on the history of the term “moral hazard” Rowell and Connelly (2012) note that the concepts of moral hazard and adverse selection have often been confused in the insurance literature. They also remark that this literature tends to attribute a pejorative meaning to “moral hazard,” often associated with fraud, in contrast to the economic literature which focuses on incentives and maintains that “moral hazard has in fact little to do with morality” (Pauly 1968).
- 33.
Ex post moral hazard is particularly important in medical insurance, where claimed expenses are dependent on decisions made by the patient and the physician once illness has occurred.
- 34.
Note that moral hazard is also present in the insurer–reinsurer relationship (see Jean-Baptiste and Santomero 2000). The success of index products in insurance securitization is partly due to the fact that they remove the moral hazard from the relationship between insurers and providers of reinsurance coverage (Doherty and Richter 2002).
- 35.
The situation is of course different in monopolistic insurance markets (see Boyer and Dionne 1989a) or in markets where retrospective rating is mandatory.
- 36.
- 37.
Dionne et al. (2011) claim to have found evidence of moral hazard in the statistical relationship between traffic violations and accumulated “demerit points” in the system of driving license suspension threat introduced in Quebec in 1978, but they do not find such evidence when they test the effect of the 1992 insurance pricing scheme on the relationship between “demerit points” and car accidents: road infractions were reduced by 15 %, with no significant effect on car accidents.
- 38.
Insurance contracts are defined in terms of price and quantity, instead of price for any quantity. Insureds reveal their class by their choice in the menu of contracts. There is no “pooling” equilibrium, but a “separating” equilibrium.
- 39.
Stiglitz (1977) studied the monopolistic insurance case. Under asymmetric information, the monopolist insurer maximizes profit by supplying a menu of disciminating contracts. At the equilibrium situation, the high risks get some consumer surplus, but the low risks are restricted to partial insurance and do not get any surplus.
- 40.
- 41.
On the other hand, Cohen (2005) finds some evidence of adverse selection for drivers with more than 3 years of driving experience.
- 42.
- 43.
See Makki and Somwaru (2001).
- 44.
- 45.
- 46.
Advantageous selection can lead to too much insurance being purchased if there are transaction costs and competition among insurers drives profits to zero. In equilibrium, the marginal cost of insurance exceeds the market price (see Einav and Finkelstein 2011). The possibility of advantageous selection was first introduced by Hemenway (1990), who termed it “propitious” selection, and analyzed later on by De Meza and Webb (2001).
- 47.
In the monopoly case, insureds cannot switch to an other insurer over time.
- 48.
- 49.
In the first period, insureds may choose either a pooling contract with partial coverage and possible renegociation in the second year, or the Rothschild–Stiglitz contract designed for high risks.
- 50.
For good risks who do not file a claim in the first period the reward takes the form of additional coverage in the second period.
- 51.
See also Bonato and Zweifel (2002) on the use of multiple risks to improve the assessment of loss probability.
- 52.
This is an example of the well-known result that additional public information may have adverse welfare consequences (see, e.g., Arrow 1978).
- 53.
In contrast, Doherty and Thistle (1996) find that additional private information has no value if there is no treatment option conditional on this information.
- 54.
Note, however, that there exists alternative views on the welfare effect of asymmetric information. Using a two-period model where insureds have the option to switch insurers in the second period, de Garidel-Thoron (2005) shows that information sharing among insurers is welfare-decreasing. The reason is that this reduces the set of viable long-term contracts available to individuals in the first period competition game.
- 55.
See also Zweifel and Ghermi (1990) for a study using Swiss data.
- 56.
Berry-Stölzle and Born (2012) provide an empirical account of the deregulation introduced in Germany in 1994. They find evidence of a significant price decrease in highly competitive lines, offset by higher prices in the other lines.
- 57.
AIG failure is mainly attributed to two causes. First, a subsidiary of AIG—AIG Financial Products—became heavily involved in the writing of credit default swaps (CDS). Second, an other subsidiary, operating in the life branch, had engaged in securities lending programs that were severely hurt by the outburst of the subprime crisis. In either case, insurance operations were not concerned.
- 58.
The Solvency II regulation is presented and analyzed in Eling et al. (2007).
- 59.
- 60.
Monti (2011) provides a recent review of public-private arrangements already existing in the OECD area.
- 61.
See Boubakri (2011) and the September 2011 Special Issue of The Journal of Risk and Insurance for a recent survey of corporate governance in the insurance industry.
- 62.
The similarity between option contracts and insurance policies was stressed by Briys and Loubergé (1983).
- 63.
- 64.
- 65.
The same kind of argument was used by Doherty and Tinic (1981) to question the motivation of reinsurance demand by insurers.
- 66.
Rochet and Villeneuve (2011) show that cash-poor firms should hedge using financial derivatives but not insure, whereas the opposite is true for cash-rich firms.
- 67.
Tobin’s Q is defined in this case as the market value of equity plus the book value of liabilities divided by the book value of assets.
- 68.
The convergence between reinsurance and investment banking was emphasized by Cummins (2005).
- 69.
The debate has regained importance after the 2008 financial market crisis and the collapse of AIG. Large insurance companies have been ranked with banks in the group of “Systemic Important Financial Institutions” (SIFI) and are threatened to be subject to the same regulations as banks. This is an occasion for the insurance industry to underline the differences between banking and insurance (see Lehmann and Hofmann 2010; Geneva Association 2010).
- 70.
Public insurance may also be justified on equity considerations, e.g., in medical insurance.
- 71.
In the USA, where a National Flood Insurance program already exists for long, and where California has established a government earthquake insurance program (the California Earthquake Authority), the possible creation of state or regional catastrophe funds is being hotly debated, given the unconvincing example of the two above-mentioned programs (see Klein and Wang 2009).
- 72.
The early options and futures on four narrow-based indices of natural catastrophes were replaced in October 1995 by call spreads on nine broad-based indices. Lewis and Murdock (1996) proposed to have the same kind of contract supplied by Federal authorities, in order to complete the reinsurance market.
- 73.
Harrington and Niehaus (1999) had reached the conclusion that basis risk would not be a significant problem for PCS derivative contracts, but later on Cummins et al. (2004) reached a different conclusion: they attibute the lack of success to basis risk. One may add that, possibly, the failure was due to the absence of arbitrage trading. Arbitrage trading between a derivative market and the market for the underlying instrument is essential to the provision of liquidity in derivatives trading for hedging and speculation purposes. However, in the case of PCS option contracts such trading was impossible. The only market for the trading of insurance portfolios is the reinsurance market, not liquid enough to be used as a vehicle in arbitrage trading.
- 74.
Exposure to moral hazard for the investor is traded against basis risk for the sponsor.
- 75.
The risk of default by the reinsurance provider is a concern in the high-layer segment of the reinsurance market.
- 76.
Still, it remains that the use of insurance-linked securities raises sensitive issues in terms of regulation. Not because these instruments would represent a danger for the stability of the financial system, but because regulators, more particularly in the USA, are reluctant to consider them as genuine alternative mechanisms for risk transfer: see Klein and Wang (2009).
- 77.
- 78.
Other innovations, such as sidecars and ILWs (Industry Loss Warranties), are different in nature from those presented in this section. They represent innovations that improve the capacity of the reinsurance market, without introducing an alternative or complement to reinsurance contracts.
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Acknowledgements
This survey is the revised and updated version of earlier surveys published as “Risk and insurance economics 25 years after” and “Developments in risk and insurance economics: the past 25 years” respectively in The Geneva Papers on Risk and Insurance—Issues and Practices (No 89, October 1998, pp. 540–567) and in Handbook of Insurance, G. Dionne (Ed.), Kluwer Academic Publishers, Boston, 2000, Chapter 1, pp. 3–33. I thank Georges Dionne, Louis Eeckhoudt, Harris Schlesinger and an anonymous reviewer for their comments on successive versions. The usual disclaimer applies.
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Loubergé, H. (2013). Developments in Risk and Insurance Economics: The Past 40 Years. In: Dionne, G. (eds) Handbook of Insurance. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0155-1_1
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