Ambiguity Aversion in the Field of Insurance: Insurers’ Attitude to Imprecise and Conflicting Probability Estimates

This article presents the results of a survey designed to test, with economically sophisticated participants, Ellsberg’s ambiguity aversion hypothesis, and Smithson’s conflict aversion hypothesis. Based on an original sample of 78 professional actuaries (all members of the French Institute of Actuaries), this article provides empirical evidence that ambiguity (i.e. uncertainty about the probability) affect insurers’ decision on pricing insurance. It first reveals that premiums are significantly higher for risks when there is ambiguity regarding the probability of the loss. Second, it shows that insurers are sensitive to sources of ambiguity. The participants indeed, charged a higher premium when ambiguity came from conflict and disagreement regarding the probability of the loss than when ambiguity came from imprecision (imprecise forecast about the probability of the loss). This research thus documents the presence of both ambiguity aversion and conflict aversion in the field of insurance, and discuses economic and psychological rationales for the observed behaviours.     

Ambiguity aversion in the small and in the large for weighted linear utility

The widely observed preference for lotteries involving precise rather than vague of ambiguous probabilities is called ambiguity aversion. Ambiguity aversion cannot be predicted or explained by conventional expected utility models. For the subjectively weighted linear utility (SWLU) model, we define both probability and payoff premiums for ambiguity, and introduce alocal ambiguity aversion function a(u) that is proportional to these ambiguity premiums for small uncertainties. We show that one individual's ambiguity premiums areglobally larger than another's if and only if hisa(u) function is everywhere larger. Ambiguity aversion has been observed to increase 1) when the mean probability of gain increases and 2) when the mean probability of loss decreases. We show that such behavior is equivalent toa(u) increasing in both the gain and loss domains. Increasing ambiguity aversion also explains the observed excess of sellers' over buyers' prices for insurance against an ambiguous probability of loss.     

Uncertainty Aversion Vs. Competence: An Experimental Market Study

Heath and Tversky (1991, Journal of Risk and Uncertainty 4:5–28) posed that reaction to ambiguity is driven by perceived competence. Competence effects may be inconsistent with ambiguity aversion if betting on own judgement is preferred to betting on a chance event, because judgemental probabilities are more ambiguous than chance events. This laboratory experiment analyses whether ambiguity affects prices and volumes in a double auction market, and contrasts ambiguity aversion to competence effects. In order to test for the presence of competence effects, in the experiment uncertainty is tied to the realisation of events about which the decision maker is more or less knowledgeable. Two experiments are presented: in the first, knowledge is exogenous, whereas in the second the knowledge judgement is endogenous. Market prices provide evidence in favour of the competence hypothesis only when competence is self-assessed. Comparable volumes are observed in both experiments.      

An Experiment on Rational Insurance Decisions

We describe the results of an experiment on decision making in an insurance context. The experiment was designed to test for the underlying rationality of insurance consumers, where rationality is understood in usual economic terms. In particular, using expected utility as the preference function, we test for positive marginal utility, risk aversion, and decreasing absolute risk aversion, all of which are normal postulates for any microeconomic decision context under uncertainty or risk. We find that there the discrepancy from rational decision making increases with the sophistication of the rationality criteria, that irrationality concerning fair premium contracts is uncharacteristically high, and that the slope of absolute risk aversion seems to depend on the format of the insurance contract. This revised version was published online in June 2006 with corrections to the Cover Date.     

The effects of loss aversion on deceptive advertising policies

We extend the deceptive advertising model of Piccolo et al. (RAND J Econ 46(3):611–624, 2015) to a framework in which consumers may be loss averse. There are two sellers, competing on prices and offering experience goods with some differences in quality. Prospective customers may be harmed by deceptive advertising: a marketing practice that can induce them to make bad purchases. We show that although deceptive advertising occurs depending on the degree of consumers’ loss aversion, this behavioral bias does not reflect on firms’ prices. Nevertheless, the presence of loss-averse consumers crucially changes the optimal deterrence rule that a Public Authority should adopt against false claims and misleading advertising. Unlike Piccolo et al. (2015), in this more general model, strong enforcements may improve the buyer welfare according to the degree of loss aversion.

     

Ambiguity aversion and the propensities for self-insurance and self-protection

Two models of ambiguity preferences that permit comparative statics analysis of greater ambiguity aversion yield definite predictions concerning propensities for self-insurance and self-protection: The levels of both activities that are optimal for an ambiguity-averse decision maker are higher in the presence of ambiguity than in its absence, and demands for both activities increase with greater ambiguity aversion. The reason is that, at levels optimal for one decision maker, an increase in either activity results in a mean-preserving contraction in the distribution of expected utility in the presence of ambiguity, which is valuable to anyone with the same risk preferences who is more ambiguity averse.     

Measuring ambiguity attitude: (Extended) multiplier preferences for the American and the Dutch population

Empirical studies of ambiguity aversion often use measures that are not grounded in theory. This paper shows how a theoretically-founded measure of ambiguity aversion can be derived from Hansen and Sargent’s theory of multiplier preferences. Multiplier preferences are used in macroeconomics to capture model uncertainty. At the micro level, they have not been applied yet, because they do not permit ambiguity seeking, which is usually observed for a substantial proportion of subjects. We give a preference foundation for (extended) multiplier preferences accommodating both ambiguity aversion and ambiguity seeking and we propose a simple method to measure them using matching probabilities. We illustrate our method in two large representative samples (Dutch and American) and obtain the first micro estimates of multiplier preferences.     

Framing,probability distortions,and insurance decisions

A series of studies examines whether certain biases in probability assessments and perceptions of loss, previously found in experimental studies, affect consumers' decisions about insurance. Framing manipulations lead the consumers studied here to make hypothetical insurance-purchase choices that violate basic laws of probability and value. Subjects exhibit distortions in their perception of risk and framing effects in evaluating premiums and benefits. Illustrations from insurance markets suggest that the same effects occur when consumers make actual insurance purchases.Presented at the Conference onMaking Decisions about Liability and Insurance, The Wharton School, University of Pennsylvania, Philadelphia, PA, 6–7 December, 1991. This research is supported by National Science Foundation Grant SES88-09299. The authors thank Jon Baron, Colin Camerer, Neil Doherty, Paul Kleindorfer, Amos Tversky, and two anonymous referees for many helpful comments. We particularly acknowledge the efforts of Matthew Robinson and Penny Pollister for their help with data analysis.     

Causes of ambiguity aversion: Known versus unknown preferences

Ambiguity aversion appears to have subtle psychological causes. Curley, Yates, and Abrams found that the fear of negative evaluation by others (FNE) increases ambiguity aversion. This paper introduces a design in which preferences can be private information of individuals, so that FNE can be avoided entirely. Thus, we can completely control for FNE and other social factors, and can determine exactly to what extent ambiguity aversion is driven by such social factors. In our experiment ambiguity aversion, while appearing as commonly found in the presence of FNE, disappears entirely if FNE is eliminated. Implications are discussed.      

Judged knowledge and ambiguity aversion

Competence has recently been proposed as an explanation for the degree of ambiguity aversion. Using general knowledge questions we presented subjects with simple lotteries in which they could bet on an event and against the same event. We show that the sum of certainty equivalents for both bets depends on the judged knowledge of the class of events. We also elicited the decision weights for events and complementary events. We found a similar effect of knowledge on the sum of decision weights.     

Ambiguity aversion and familiarity bias: Evidence from behavioral and gene association studies

It is increasingly recognized that decision making under uncertainty depends not only on probabilities, but also on psychological factors such as ambiguity and familiarity. Using 325 Beijing subjects, we conduct a neurogenetic study of ambiguity aversion and familiarity bias in an incentivized laboratory setting. For ambiguity aversion, 49.4% of the subjects choose to bet on the 50–50 deck despite the unknown deck paying 20% more. For familiarity bias, 39.6% choose the bet on Beijing’s temperature rather than the corresponding bet with Tokyo even though the latter pays 20% more. We genotype subjects for anxiety-related candidate genes and find a serotonin transporter polymorphism being associated with familiarity bias, but not ambiguity aversion, while the dopamine D5 receptor gene and estrogen receptor beta gene are associated with ambiguity aversion only among female subjects. Our findings contribute to understanding of decision making under uncertainty beyond revealed preference.     

Intertemporal utility smoothing under uncertainty

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai (Econometrica 76:137–153, 2008) model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler (J Math Econ 18:141–153, 1989) multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.     

Are the poor worse at dealing with ambiguity?

This paper studies the relationship between people’s ambiguity attitudes and income in the field using language as a natural source of ambiguity. It shows that the method of Baillon et al. (2017b) can be adapted for field studies, providing ambiguity measurement tasks that are more comprehensible for nonacademic subjects. Ambiguity attitudes were elicited in two groups of Chinese adolescents (poor rural and rich urban), among whom the income variation is big. In the rural group the poorer are both more ambiguity averse and more a-insensitive, whereas in the urban group the richer are more a-insensitivite. On average, the poor rural adolescents are worse at dealing with ambiguity than their urban counterparts. A-insensitivity, which measures people’s understanding of an ambiguous situation, is an important but sometimes neglected component of ambiguity attitude. Policies aiming to help people improve decisions may focus more on reducing a-insensitivity as this cognitive bias is more likely to be influenced by intervention than people’s intrinsic aversion towards ambiguity.     

Dynamic awareness and zero probability beliefs

We study behavioral patterns of insurance demand for low-probability large-loss events (catastrophic losses). Individual patterns of belief formation and risk attitude that were suggested in the behavioral decisions literature emerge robustly in the current set of insurance choices. However, social comparison effects are less robust. We do not find any evidence for peer effects (through social-loss aversion or imitation) on insurance take-up. In contrast, we find support for the prediction that people underweight others’ relevant information in their own decision making.     

Hopes and Fears: the Conflicting Effects of Risk Ambiguity

The Ellsberg Paradox documented the aversion to ambiguity in the probability of winning a prize. Using an original sample of 266 business owners and managers facing risks from climate change, this paper documents the presence of departures from rationality in both directions. Both ambiguity-seeking behavior and ambiguity-averse behavior are evident. People exhibit fear effects of ambiguity for small probabilities of suffering a loss and hope effects for large probabilities. Estimates of the crossover point from ambiguity aversion (fear) to ambiguity seeking (hope) place this value between 0.3 and 0.7 for the risk per decade lotteries considered, with empirical estimates indicating a crossover mean risk of about 0.5. Attitudes toward the degree of ambiguity also reverse at the crossover point.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

Ambiguity and the value of information

The value of information is studied in a non-expected utility model of ambiguity with second-order probabilities. Information that reduces ambiguity has a positive value for ambiguity-averse decision makers, and the value of information that resolves ambiguity increases with greater ambiguity and with greater ambiguity aversion. Since information that resolves risk is valuable, and must also resolve ambiguity, the value of such information for ambiguity averters increases with greater ambiguity and with greater ambiguity aversion.     

Ambiguous life expectancy and the demand for annuities

In this paper, ambiguity aversion to uncertain survival probabilities is introduced in a static life-cycle model with a bequest motive to study the optimal demand for annuities. Provided that annuities’ return is sufficiently large, and notably when it is fair, positive annuitization is known to be the optimal strategy of ambiguity neutral individuals. Conversely, we show that the demand for annuities decreases with ambiguity aversion and that there exists a finite degree of aversion above which the demand is non-positive: the optimal strategy is then to either sell annuities short or to hold zero annuities if the former option is not available. To conclude, ambiguity aversion appears to be a relevant candidate for explaining the annuity puzzle.     

The catastrophic effects of natural disasters on insurance markets

Natural disasters often have catastrophic risks on insurance companies as well as on the insured. Using a very large dataset on homeowners’ insurance coverage by state, by firm, and by year for the 1984 to 2004 period, this paper documents the positive effect on losses and loss ratios of both unexpected catastrophes as well as large events that the authors term “blockbuster catastrophes.” Insurers adapt to these catastrophic risks by raising insurance rates, leading to lower loss ratios after the catastrophic event. There is a widespread event of unexpected catastrophes and blockbuster catastrophes that reduces total premiums earned in the state, reduces the total number writing insurance coverage in the state, and leads to the exit of firms from the state. Firms with low levels of homeowners’ premiums are most adversely affected by the catastrophes.     

Adverse Selection,Bequests, Crowding Out,and Private Demand for Insurance: Evidence from the Long-term Care Insurance Market

Adverse selection, moral hazard, and crowding out by public insurance have all been proposed as theoretical reasons for why the market for private long-term care insurance has been slow to evolve in the U.S. Using national samples of the elderly and near elderly, this study investigates which is most important. The data contain direct measures of risk aversion, expectations of future nursing home use and living to old age, and the bequest motive. For both groups, we find evidence of adverse selection, and, for the elderly, crowding out of private long-term care insurance by Medicaid. However, we do not find that demand for such insurance is motivated either by bequest or exchange motives.