Quantifying Food Deficit Risk under Seasonal Climate Variability Using a Compound Periodic Poisson Process

Abstract

Climate variability has increased the frequency of extreme weather events, leading to greater uncertainty in agricultural production and a higher risk of food production deficits. Existing studies predominantly employ deterministic or econometric approaches that estimate average production changes without explicitly quantifying stochastic production risk. This study proposes a compound periodic Poisson process framework to quantify climate induced food production risk by integrating periodic event occurrence, stochastic loss severity, aggregate production loss, and food deficit probability within a unified actuarial framework. The occurrence extreme rainfall events are modelled using a periodic Poisson process, while production loss severity follows a Lognormal distribution. Model parameters are estimated using Maximum Likelihood Estimation, and food deficit probabilities are evaluated analytically. The estimated seasonal intensity ranges from 25 to 53 events per month during the rainy season to 1 event per month during the dry season. The expected aggregate production loss is 18.420 tons per planting season. For a critical production loss threshold of 25.000 tons, the estimated probability of food production deficit is 17,6%, corresponding to a return period of 5,68 planting seasons. These results demonstrate that the proposed compound periodic Poisson process provides a robust probabilistic framework for agricultural risk assessment, food security analysis, and climate based agricultural insurance.