Insurance Market Under Ambiguity

In the21st century, natural disasters are increasingly frequently, which results inmore and more insured losses. However, research in this area is relative lack because oflacking ripe theory. In China, this problem is particularly prominent. So, we have a freshlook at these problems that optimal insurance demand and market equilibrium in a simpleinsurance model, where the distribution of the actual loss probabilities is unknown to bothinsurers and the insured, and the insurer is risk-neutral and ambiguity-averse, while theinsured is risk-averse and ambiguity-averse.Compared with the traditional research ignoring the impact of ambiguity whobelieves that there is a positive relation between the demand for insurance and riskprobability, we have found that an increase in risk does not necessarily increase thedemand for insurance in the presence of ambiguity. It all depends on the degree ofambiguity aversion. That is to say, if the ambiguity preferences exhibit constant ordecreasing ambiguity aversion, then an increase in risk will increase the demand forinsurance. Otherwise, an increase in risk will decrease the demand for insurance.Moreover, if the consumers are ambiguity-averse, the optimal insurance contract is fullinsurance without considering the deductible.Furthermore, it is demonstrated that if insurers are equally or less ambiguous thanthe insured, a unique equilibrium exists, and full insurance will be purchased. If insuresare more ambiguous than the insured, no insurance may be purchased.