Non-expected-utility (EU) preferences
The literature on non-EU preferences in optimal insurance is considerably thinner than the literature on optimal insurance with EU preferences. Modern non-EU preferences include Yaari’s dual theory, rank-dependent utility theory as well as cumulative prospect theory. Optimizing the interests of policyholder and insurer based on non-EU preferences still has room for investigation.
In most past literature, it was usually assumed that the policyholder and insurer have common belief regarding the loss distribution. Going beyond this framework, the classical results would no longer hold optimal. How to incorporate into the model the heterogeneous beliefs among the policyholder, insurer as well as reinsurer is appealing to both the academics and practitioners.
In practice, both the policyholder and insurer face some ambiguity (uncertainty) about the distribution of their potential losses. It has been well documented that an individual's decision-making is affected by such ambiguity (e.g., Ellsberg's paradox). Some recently developed models, e.g. maxmin EU model, α-maxmin EU model, Choquet integral as well as smooth ambiguity model, attempt to explore the decision-making strategy within an ambiguous environment. The application of these models in complicated insurance design is not widespread.
Traditionally, decision maker is assumed to apply either EU maximization or risk minimization to choose insurance policy. It is understandable that these two objective functions are not mathematically compatible, however it is of practical sense to combine them in the decision-making process. This is very much related to how to strike a balance between the conflicting objective functions, which is another interesting branch of optimal insurance design problem.
Although my current works focus on static problems, I intend to extend them to dynamic ones. In such a case, dynamic programming and optimal control methodologies for stochastic processes could be applied. The financial risks could also be incorporated into the insurance models.