A Study of Underwriting Decision Making Based on ARIMA Modeling with Composite Poisson Processes

Abstract

Facing the problem of frequent occurrence of natural disasters, how to accurately predict the scale of loss and the probability of insolvency is the key for insurance companies to reduce risk and optimize underwriting strategies. This paper explores the multiple influencing factors of catastrophe risk and works to establish a practical risk prediction model. The model is divided into two parts: the first part uses ARIMA model to predict the risk loss, considering the influence of disaster factors, vulnerability, exposure, and disaster prevention ability on the risk size; the second part establishes a positive risk model based on the bankruptcy theory, and assumes that the insurance enrollment process is a composite Poisson process, and constructs a model of the claims process. The probability of insolvency for each year is estimated by substituting the predicted loss values into the claims model and calculating the initial and annual premiums. The study conducted a five-year risk prediction for the Philippines and Australia, and the results show that there is a significant difference in disaster risk management between the two countries, which provides a theoretical basis and practical guidance for subsequent underwriting recommendations.