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Efficient Parameter Estimation for Claim-Time Behaviour in Insurance Portfolios: MCMC Simulation Analysis of MLE and MAP Techniques
Estimación eficiente de los parámetros del comportamiento siniestral de las carteras de seguros: Análisis de simulación MCMC de las técnicas MLE y MAP.
DOI:
https://doi.org/10.15446/rce.v48n2.114887Keywords:
Bayesian Inference, Maximum Likelihood Estimation, Maximum a-Posteriori, Markov Chain Monte Carlo Simulation. (en)Estimación de máxima verosimilitud, Inferencia bayesiana, Maximum a posteriori, Simulación Monte Carlo con cadenas de Markov (es)
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The study investigated the dynamics of _commencement-to-event-time-behaviour in life insurance portfolios, employing Maximum Likelihood Estimation (MLE) and Maximum A Posteriori (MAP) with the Markov Chain Monte Carlo (MCMC) simulation technique. Focusing on the Lognormal and Exponential distributions for their efficacy in modelling time-to-occurrence data, the research simulated 120 observations from both distributions and estimated parameters using the first 80 ordered samples. Remarkably, estimates for lognormal parameters obtained through MLE and MAP_MCMC were highly similar, with errors well within 10% of the actual values, highlighting the accuracy of both methods. The study also explored the robustness of the MAP_MCMC technique to various prior distributions, demonstrating its effectiveness across different priors, including Exponential, Normal, Gamma, Pareto, and Weibull prior distributions. In the case of the exponential distribution, both MLE and MAP_MCMC techniques performed exceptionally well, providing estimates within 5% of the true value, with MAP _MCMC exhibiting remarkable precision, just 1% off the true value. Real-life data fitted to the Gamma distribution showed that MLE and MAP _MCMC methods, using censored data, closely approximated benchmark estimates from the method of moments. The MAP_MCMC approach slightly outperformed the MLE.
El estudio investigó la dinámica del comportamiento “inicio-acontecimiento-tiempo” en las carteras de seguros de vida, empleando la Estimación de Máxima Verosimilitud (MLE) y la Máxima A Posteriori (MAP) con la técnica de simulación Markov Chain Monte Carlo (MCMC). Centrándose en las distribuciones Lognormal y Exponencial por su eficacia en la modelización de datos de tiempo de ocurrencia, la investigación simuló 120 observaciones de ambas distribuciones y estimó los parámetros utilizando las 80 primeras muestras ordenadas. Sorprendentemente, las estimaciones de los parámetros lognormales obtenidas mediante MLE y MAP_MCMC fueron muy similares, con errores muy inferiores al 10% de los valores reales, lo que pone de relieve la precisión de ambos métodos. El estudio también exploró la robustez de la técnica MAP_MCMC a varias distribuciones a priori, demostrando su eficacia a través de diferentes distribuciones a priori, incluyendo Exponencial, Normal, Gamma, Pareto y Weibull. En el caso de la distribución exponencial, tanto las técnicas MLE como MAP_MCMC obtuvieron resultados excepcionales, proporcionando estimaciones dentro del 5% del valor real, con MAP_MCMC mostrando una precisión notable, sólo un 1% por debajo del valor real. Los datos reales ajustados a la distribución Gamma mostraron que los métodos MLE y MAP_MCMC, utilizando datos censurados, se aproximaron mucho a las estimaciones de referencia del método de los momentos. El método MAP_MCMC superó ligeramente al MLE.
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