Tags: Ambiguity, Economic premium principle, Equilibrium, Expected Utility with Uncertain Probability (EUUP), IRFRC
More from: Hideki Iwaki

This paper considers a pure exchange economy with insurance against ambiguous loss. Here, ambiguity means a condition in which probabilities of possible events are not uniquely assigned. Although the search for models of decision making and insurance pricing under ambiguity has been evolving toward the ultimate separations between risk and ambiguity, the existing models still remains some relation between risk and ambiguity and the search for an applicable model is still ongoing.

This paper further develops a model of pricing insurance or an economic premium principle that can be used in empirical and behavioral studies by refining the separations between tastes and beliefs, and between risk and ambiguity.

To this ends, we adopt a new decision-making model called Expected Utility with Uncertain Probability (EUUP) theory of Izhakian in 2017 to represent preference of agents. EUUP can completely distinguishes tastes from beliefs and risk from ambiguity. It can identifies the sources of uncertainty, allowing attitude toward ambiguity to be completely elicited.

We show that the equilibrium uniquely exists in this economy. Then, we derive the equilibrium insurance premium, which can be viewed as a generalization of traditional Buhlmann’s economic premium principle under EUUP. We also study the effects of ambiguity on both optimal insurance demand and premium through comparative statics analysis.

Through comparative statics analysis, we numerically confirm that insurance transactions or risk exchanges occur due to the difference in the degree of ambiguity aversion even if all the agents are either ambiguity averse or ambiguity loving as well as they share the same attitude toward risk.

These results are our main contribution compared with existing literature. Chatauneuf et. al. (2000) and Tsanakas and Christofides (2006) say optimal insurance demand or risk sharing is comonotonic in equilibrium under Choquet Expected Utility (CEU) or Maxmin Expected Utility (MEU) assuming that all agents in economy are ambiguity averse. However, our results show that their assertion does not necessarily hold.

Furthermore, existing models show sufficient conditions such that an increase in ambiguity aversion increases both demand and premium for insurance, however, it is difficult to confirm whether this condition actually holds even if we specify the form of utility function, and it is also difficult to explicitly derive the result numerically.

On the other hand, as we can explicitly derive results numerically in our model, it is much easier to apply them to empirical studies and experiments compared to existing model.

The results give some explanations for the equity premium puzzle such that actually observed risk premium of stocks is so large that it cannot be explained by the standard economic models, as well as the experimental results such as Sarin and Weber (1993) that individual bids and market prices for lotteries with ambiguous probabilities are consistently lower than the corresponding ones with well-defined probabilities.

Furthermore, as to Japanese insurance market, premiums of life-insurance are said to be higher than those fair values. Consequently, our model may shed light on these problems if the discrepancy occurs due to ignoring effects of ambiguity .

The complete paper is available for download https://ssrn.com/abstract=3102816.