The Effect of Ambiguity Aversion on Insurance and Self‐protection

Abstract

In this article, we derive a set of simple conditions such that ambiguity aversion always raises the demand for self-insurance and the insurance coverage, but decreases the demand for self-protection. We also characterise the optimal insurance design under ambiguity aversion and exhibit a case in which the straight deductible contract is optimal as in the expected utility model. Almost all models used in insurance economics up to now have been based on subjective expected utility theory. Therefore, this literature has assumed that ambiguity over probabilities does not matter for decisions. This assumption is inconsistent with many experimental results (Camerer, 1995). The most famous observation illustrating violation 6 of the subjective expected utility theory is the Ellsberg (1961) paradox. The paradox can be explained by ambiguity aversion, which can be thought of as an aversion to any mean-preserving spread in the space of probabilities. For example, ambiguityaverse agents prefer the lottery that yields a specific gain with a probability 1/2 to another lottery, in which the probability of earning the same gain is uncertain, but with a subjective mean of 1/2 (e.g. if the agent believes that the probability is either 1/4 or 3/4 with equal probability); see for example, Halevy (2007) for recent experimental evidence. This psychological trait differs from risk aversion, which is an aversion to any mean-preserving spread in the pay-off of the lottery. Since the seminal work by Gilboa and Schmeidler (1989), decision theorists have proposed various decision models that exhibit a form of ambiguity aversion (for a literature survey, see Etner et al., (2012)).In this article, we study the effect of ambiguity aversion on insurance and selfprotection decisions using the theory of ambiguity axiomatised by Klibanoff et al. (2005). This theory captures the idea that mean-preserving spreads in probabilities reduce the welfare of ambiguity-averse agents. Also, this theory permits us to separate the effect of ambiguity aversion from that of risk aversion. Therefore, our results permit us to examine whether the effect of ambiguity aversion on insurance and self-protection differs from that of risk aversion.Several papers have studied the effect of risk aversion on insurance and self-protection within the subjective expected utility model. A well-known result is that risk aversion increases the demand for insurance, that is, it raises the coverage rate, and it reduces the straight deductible. Indeed, in the case of coinsurance, this result is a direct

The Impact of Ambiguity Prudence on Insurance and Prevention

“…8 Remark that in the single period model studied by Alary, Gollier, and Treich (2013), this willingness to pay P is nothing but what Berger (2011) or Maccheroni et al (2013) call the uncertainty premium, which is by definition superior to Pratt's risk premium under ambiguity aversion.…”

“…In a recent contribution, Alary, Gollier, and Treich (2013) introduced the notion of ambiguity in self-insurance and self-protection models. By extending a work initiated by Snow (2011), they offered these tools originally designed for the study of risks a broader scope of application.…”

“…It is both an extension of Snow (2011) and Alary, Gollier, and Treich (2013) in the sense that it goes from the study of the one-to the two-period problem, and of Menegatti (2009) and Berger (2010) in the sense that it allows non neutral ambiguity attitudes.…”

Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer

“…For example, Alary et al [15] examine a problem of optimal insurance design in which the insured is ambiguity-averse in the sense of Klibanoff, Marinacci and Mukerji [16]. The authors assume that, conditional on a non-zero loss occurring, the loss severity distribution is not ambiguous; however, the probability that a loss occurs is ambiguous.…”

Ambiguity on the insurer’s side: The demand for insurance

“…As such, it is very different from what we do in this paper. For instance, Alary et al [1] consider an insured who is ambiguityaverse in the sense of Klibanoff, Marinacci, and Mukerji [31], and assume that the ambiguity is concentrated only in the probability that a loss occurs. Conditional on a loss occurring, the distribution of the loss severity is unambiguous.…”