A new robust insurance model considering the time of accident

Abstract

The principle of maximum utility is generally adopted to design the optimal insurance contracts, which should consider the influence of different factors such as the probability of accident, premium, compensation, and so on. However, most literatures deal with these variables from a static perspective. This paper considers the accident probability and the value of insurance subject based on the time of accident, which is rarely involved in the previous studies and considers the utility function of the insurer and the policyholder from a dynamic perspective. Firstly, to make this model more universally applicable, we establish an insurance model that considers the time of the accident and different premium payment forms for policy-holders and insurers respectively. Next, we derive a robust premium insurance model based on min-max regret, in which the time of the accident can be assumed to be certain and uncertain respectively. Then, we conduct numerical experiments and analyze the utility of the policy-holders, demonstrating guarantee period and value of insurance subject are significant when insuring and derive the optimal coverage rate. These results also show that the insurance model that takes into account the time of accident performs better.