Probability of Motor Vehicle Insurance Bankruptcy Using a Recursive Model in the Discrete Time Surplus Process

Early bankruptcy prediction is crucial in the motor vehicle insurance industry. The use of Poisson distribution in classical insurance theory models is often difficult to solve analytically for more complex claim distributions. Therefore, models with a discrete time-based approach can be used as an alternative. This study applies Cruz et al.'s (2024) recursive method to the Swedish Motor Insurance Dataset to calculate and analyze the probability of bankruptcy in motor vehicle insurance. The results show that the recursive model produces very high accuracy (R² = 0.9999) with a bankruptcy probability ψ(1) = 74.59% that decreases dramatically to 0.000461% at ψ(100). A minimum initial capital of 37 units is required to achieve a risk target below 1%, with a decay rate of 12.91% per unit of capital. The simple approximation formula proved to be effective as a quick tool for capital planning with a MAPE of 9.08%. This study concludes that the discrete-time recursive approach is not only simpler and more flexible, but also provides valuable quantitative guidance for better risk management and capital allocation decisions in the face of bankruptcy risk.