Compound Poisson–Lindley process with Sarmanov dependence structure and its application for premium-based spectral risk forecasting

Abstract

One of the fundamental challenges insurance companies face is forecasting a fair premium that covers the cost of claims while maintaining profitability. To comprehend the risk of insurance claims, one needs to construct a collective risk model. In this study, we aim to propose a new collective risk model, namely a dependent compound Poisson–Lindley process. We capture the dependence structure between the claim frequency and severity using a bivariate Sarmanov distribution. We then employ this model to perform premium-based risk measure forecasting such that the insurance company can obtain the premium value for the policyholder. We accomplish this task by proposing a specific risk spectrum to adjust the premium for risk-aversion-type insurance companies. Our main results demonstrate that a collective risk model based on the Poisson–Lindley process is able to capture the overdispersion phenomenon in claim frequency that is common in practice. This ability is confirmed by our simulation conducted using real insurance data. Furthermore, when accounting for the Sarmanov dependence structure, the resulting premium value becomes more appropriate.