Stochastic reserving using policyholder information via EM algorithm

Abstract

In stochastic reserving, the incurred outstanding liabilities of general insurance companies result in incomplete claims because of truncation and censoring. It is necessary for insurance companies to predict liabilities in risk management. We propose a model that allows the incorporation of heterogeneity among policies, which is important for loss reserving. The incompleteness of observation data leads us to use expectation-maximization (EM) algorithm to obtain the maximum likelihood estimations of the parameters of the model. We also show that the deviation of loss reserving from the loss reserve weakly converges to a normal distribution at the rate m, where m is the size of the risk portfolio. A simulation study is conducted to compare the proposed method with the ones without policyholder’s information as well as obtained by chain ladder method and compare the convergence rates of EM algorithm and the direct maximization by Newton-Raphson method. We also analyse real-life health insurance data to illustrate the use of the method in practice.