Efficient Parameter Estimation for Claim-Time Behaviour in Insurance Portfolios: MCMC Simulation Analysis of MLE and MAP Techniques

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 MAPMCMC 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 MAPMCMC 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 MAPMCMC 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 MAPMCMC approach slightly outperformed the MLE.