A Compound Cyclic Poisson Stochastic Model for Premium Determination in Weather Indexed Agricultural Insurance: Case Study in South Sulawesi, Indonesia

The agricultural sector in developing countries is highly susceptible to significant losses due to weather variability and seasonal risks. Existing premium calculation methods often rely on homogeneous risk assumptions, which fail to account for claim patterns that are highly dependent on agricultural seasonality. This limitation often leads to mispriced premiums, deterring farmer participation in crucial insurance schemes. To address this, our study proposes and analyzes a compound cyclic Poisson model designed to estimate agricultural insurance premiums under weather-dependent shocks. The model explicitly integrates seasonal variations in claim frequency and severity, aligning premium calculation with actual agricultural risk profiles. Our approach uses a quantitative, stochastic modeling method based on a compound cyclic Poisson process, which effectively captures cyclical claim patterns that correspond with planting and harvesting seasons. As a case study, the research was conducted in South Sulawesi province, an ideal representation of an agrarian region with high weather risk intensity. The weather index used in this study combines rainfall and temperature indicators to better represent climate-induced risks. Through simulations, we found that the insurance premium, derived from our model, ranges from IDR 36,796 during low weather index conditions to IDR 328,713 during high weather index conditions, approximately 20-80% below the fixed AUTP market premium of IDR 180,000. This flexible pricing range allows farmers to choose the most suitable policy for their risk level and empowers insurance companies to set fair and financially sustainable premiums, ultimately encouraging broader participation in agricultural insurance. The originality of this study lies in the integration of a compound cyclic Poisson process to model seasonal claim dynamics in agricultural insurance. This approach contributes to the literature by providing a stochastic framework that bridges theoretical modelling and practical premium calibration under real world weather variability.