Modelling Withdrawal Risk in Insurance Using a Convolutions Approach
Onchere Walter *
Department of Mathematics and Actuarial Science, Kisii University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Insurance companies are required to have reliable estimates of withdrawal probabilities or lapse rates for planning purposes. Some insurers are not able to adopt advanced methodologies given the misconceptions of the best techniques in modelling. The standard convolutions parametric distribution is the Poisson, but this distribution is effectively applied when the lapse rates are low especially in developed economies. Advancing the work of previous researchers, this manuscript applies the negative-binomial-geometric convolutions mixture to carry out withdrawal risk modelling which represents variance that exceeds its mean and better explains high lapse rates for developing economies. We generate the predicted withdrawal distribution for a variety of cases using convolutions approach. Further, we have examined various cases to check the models behaviour. The results shows that the model explains various effects of withdrawal probability on customer size and as well as withdrawal size. The performance of the model was very well justified. We advice organizations to apply this risk management methodology since its very practical.
Keywords: Withdrawal risk management, convolutions approach, withdrawal probability, bayesian criterion, negative binomial distribution