Modelling of survival time of life insurance policies in India: a comparative study

Persistency has always been the area of grave concern over the decades in insurance sector. To model the same one would initially make utilization of regression approach but that could not serve the purpose of identifying the risk factors and time trends which affect persistency. For this purpose, one should make use of survival models which account for censored data. But there are still certain concerns utilizing conventional survival models. One of which is left truncation of insurance data. Another concern is the large portfolios and absolute numbers involved in insurance sector. Thus, conventional survival models could not be adjusted for convergence when applied to such large portfolios and absolute numbers like amount of Sum Assured (SA), therefore, justifying the application of actuarial laws to model the problem. Objective of this paper is to make a comparative study between survival models and actuarial models to model persistency, so that the validity and robustness of the actuarial models may be established in case of analyzing the insurance phenomenon. Models which seem to be the best fitted models have been checked diagnostically for validity also. For this purpose, the plots of standardized residuals have been studied for randomness. To deal with dynamic structure of insurance data, stratifications have been used as per different criteria given by Insurance Regulatory and Development Authority of India (IRDAI) also. AIC values under each stratum have been weighted and then averaged to arrive at single value underneath each specification. It is found that actuarial models are robust in all cases and valid too. In fact, the choice of best fitted actuarial model has not been changed from case to case. Throughout our study only Gompertz curve fitted well to the data and is also found to be valid. The nature of relationships of Age and SA with persistency is found to be positive.