Abstract
This chapter reviews the evolution in risk and insurance economics over the past 50 years, first recalling the situation in 1973 and then presenting the developments and new approaches that have flourished since then. We argue 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 and original data to illustrate new theories but also inspiring new ideas that are relevant to the overall economy.
This survey is the revised and updated version of earlier surveys published by Henri Loubergé as “Risk and Insurance Economics 25 Years After” and “Developments in Risk and Insurance Economics: The Past 40 Years,” respectively, in The Geneva Papers on Risk and Insurance—Issues and Practices (No. 89, October 1998, pp. 540–567) and in the Handbook of Insurance, Second edition, G. Dionne (Ed.), Springer, 2013, Chapter 1, pp. 1–40. We thank Louis Eeckhoudt, Harris Schlesinger, and Richard Peter for their comments on successive versions and Claire Boisvert for the preparation of this version. The usual disclaimer applies.
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Notes
- 1.
Note that three of these seven authors, George Akerlof, Kenneth Arrow, and Gary Becker, later received the Nobel Prize in Economic Sciences.
- 2.
- 3.
Actually, Borch’s theorem was already present in Borch (1960), but the 1960 article was primarily written for actuaries, whereas the 1962 Econometrica paper was addressed to economists.
- 4.
- 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 of 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 management 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 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 can be resolved if one introduces differential risk perceptions. 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 paper shows that full insurance is not optimal under fair insurance pricing and that the usual comparative statics resulting 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.
Hong et al. (2011) argued 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 focusing on coinsurance, they showed 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 is closely linked to the literature on the demand for a risky asset, which was pioneered by Arrow (1963) 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).
- 17.
This case corresponds to a negative cross-derivative of the two-attribute utility function (u12 ≤ 0). Eeckhoudt et al. (2007) showed that this is equivalent to “correlation aversion,” i.e., the aversion to losses simultaneously affecting the two attributes of utility (health and wealth, for example).
- 18.
Following Eeckhoudt et al. (2007), the individual is then “correlation loving.” For that individual, 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 (1998) 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.
- 23.
See Schlesinger (2013) for a survey on insurance demand.
- 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 recent models are becoming very complex without generating less ambiguous results (Peter 2021a). A probability of loss equal to (greater than, lower than) 0.5 remains a crucial threshold for comparative statics analysis because it affects the direction of the variation of the variance and other statistical moments when we change the probability of loss in a two-state model. Moreover, it is not dependent on decision-makers’ risk behavior.
- 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 paper by Lee (2012), it has focused 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, because the analysis of the latter case is more straightforward even if it is often applied in principal-agent models.
- 27.
See also Wang and Li (2015).
- 28.
But, like previous work, it deals with self-protection, leaving self-insurance aside.
- 29.
See also the Geneva Risk Economics Lecture presented by Bleichrodt (2022) for another review with an emphasis on nonexpected utility. He also discusses how empirical research may help to understand the prevention puzzle.
- 30.
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.
- 31.
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 had been inappropriate.
- 32.
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.
- 33.
This result is reminiscent of the same result obtained under Hurwicz’s model of choice under risk: see Briys and Loubergé (1985).
- 34.
An economic equilibrium is first-best efficient if it is Pareto optimal: it is impossible to organize a reallocation of resources that 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 within a competitive economic system. In an efficient equilibrium, market prices reflect social opportunity costs.
- 35.
In an interesting article on the history of the term “moral hazard,” Rowell and Connelly (2012) noted that the concepts of moral hazard and adverse selection have often been confused in the traditional insurance literature. They also remarked that this literature tends to attribute a pejorative meaning to “moral hazard,” often associating it 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).
- 36.
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. It is also important in workers’ compensation and in auto bodily injury insurance.
- 37.
Dionne (1982) pointed out that moral hazard is also present when the insured event results in nonmonetary losses, for example the loss of an irreplaceable commodity.
- 38.
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).
- 39.
The situation is of course different in regulated markets where information on retrospective rating is shared by the market.
- 40.
- 41.
Insurance contracts are defined in terms of price and quantity, instead of price for any quantity. Insureds reveal their class by their choice from the menu of contracts, such as the choice of a deductible.
- 42.
Stiglitz (1977) studied the monopolistic insurance case. Under asymmetric information, the monopolist insurer maximizes profit by supplying a menu of discriminating 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.
- 43.
- 44.
- 45.
- 46.
See Makki and Somwaru (2001).
- 47.
- 48.
- 49.
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 it was later analyzed by De Meza and Webb (2001).
- 50.
Note, however, that there exist 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) showed that information sharing among insurers is welfare-decreasing. This is because it reduces the set of viable long-term contracts available to individuals in the first-period competition game.
- 51.
- 52.
In the first period, insureds may choose either a pooling contract with partial coverage and possible renegotiation in the second year, or the Rothschild-Stiglitz contract designed for high risks.
- 53.
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.
- 54.
See also Bonato and Zweifel (2002) on the use of multiple risks to improve the assessment of loss probability.
- 55.
See Crocker et al. (2025) for a recent survey.
- 56.
See Dionne and Rothschild (2014) for a framework to evaluate the economic consequences of legalized and banned risk classification systems, both in a static environment and a dynamic environment with learning.
- 57.
This is an example of the well-known result that additional public information may have adverse welfare consequences (see, e.g., Arrow 1978).
- 58.
In contrast, Doherty and Thistle (1996) found that additional private information has no value if there is no treatment option conditional on this information.
- 59.
See also Zweifel and Ghermi (1990) for a study using Swiss data.
- 60.
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.
- 61.
AIG’s 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. Second, another subsidiary, operating in the life branch, had engaged in securities-lending programs that were severely hurt by the onset of the subprime crisis. In either case, insurance operations were not concerned.
- 62.
- 63.
See Harrington et al. (2013) for a survey of the literature.
- 64.
- 65.
Monti (2011) provides a recent review of public–private arrangements that already exist in the OECD area.
- 66.
- 67.
The similarity between option contracts and insurance policies was stressed by Briys and Loubergé (1983).
- 68.
- 69.
- 70.
The same kind of argument was used by Doherty and Tinic (1981) to question the motivation of reinsurance demand by insurers.
- 71.
Rochet and Villeneuve (2011) showed that cash-poor firms should hedge using financial derivatives but not insure, whereas the opposite is true for cash-rich firms.
- 72.
- 73.
The convergence between reinsurance and investment banking was emphasized by Cummins (2005).
- 74.
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 become subject to the same regulations as banks. This is an occasion for the insurance industry to underscore the differences between banking and insurance (see Lehmann and Hofmann 2010; Geneva Association 2010).
- 75.
Public insurance may also be justified by equity considerations, e.g., in medical insurance.
- 76.
Adding collateralized reinsurance, ILWs, sidecars, and other financial coverage products, the outstanding international volume is at about $60B (Artemis website).
- 77.
In the US, where a National Flood Insurance program has already existed 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 examples of the two abovementioned programs (see Klein and Wang 2009).
- 78.
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.
- 79.
Harrington and Niehaus (1999) had reached the conclusion that basis risk would not be a significant problem for Property Claims Services (PCS) derivative contracts, but later on, Cummins et al. (2004) reached a different conclusion, attributing the lack of success to basis risk. One might 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, which is not liquid enough for use as a vehicle in arbitrage trading.
- 80.
The pricing of these contracts was addressed by Perrakis and Boloorrforoosh (2018).
- 81.
Exposure to moral hazard for the investor is traded against basis risk for the sponsor.
- 82.
The risk of default by the reinsurance provider is a concern in the high-layer segment of the reinsurance market.
- 83.
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 US, are reluctant to consider them as genuine alternative mechanisms for risk transfer: see Klein and Wang (2009).
- 84.
- 85.
- 86.
Other innovations, such as sidecars and ILWs, are different in nature from those presented in this section. They are innovations that improve the capacity of the reinsurance market, without introducing an alternative or complement to reinsurance contracts.
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Loubergé, H., Dionne, G. (2025). Developments in Risk and Insurance Economics: The Past 50 Years. In: Dionne, G. (eds) Handbook of Insurance. Springer, Cham. https://doi.org/10.1007/978-3-031-69561-2_1
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Keywords
- Insurance economics
- Optimal insurance protection
- Optimal self-protection
- Insurance pricing
- Insurance demand
- Economics of risk and uncertainty
- Financial economics
- Risk management
- Asymmetric information
- Insurance markets
- Climate finance