Nonparametric Estimation of Laplace Transform of the Ruin Probability from Empirical Data Using symmetric Kernel

This paper addresses the estimation of ruin probability, a central issue in actuarial science and financial risk management. A major difficulty lies in the limited knowledge of the claim size distribution, which often restricts the applicability of classical parametric methods. To overcome this, we introduce a nonparametric kernel estimator for the Laplace transform of the new finite-time ruin probability in the classical Cram´er– Lundberg model. The asymptotic properties of the estimator are investigated through the computation of the Mean Integrated Squared Error (MISE), highlighting improved accuracy and stability compared to traditional approaches. Simulation studies confirm the method’s reliability and robustness across different scenarios. Beyond its theoretical contribution, the results provide insurers with more flexible and accurate tools for risk evaluation and financial stability assessment.