Document Type : Journal of Mathematics and Modeling in Finance (JMMF)


1 Department of Actuarial Science, Shahid Beheshti University, Theran, Iran

2 Department of Actuarial Science, Shahid Beheshti University, Tehran, Iran


‎An important question in non life insurance research is the ‎estimation of number of future payments and corresponding ‎amount of them. A ‎loss reserve is the money set aside by insurance companies to pay ‎policyholders claims on their policies. The policyholder behavior for reporting claims after its ‎occurrence have significant effect on the costs of the insurance ‎company. This article considers the problem of predicting the amount and number ‎of claims that have been incurred but not reported, ‎say IBNR‎. ‎Using the delay probabilities in monthly level, ‎calculated by the Zero Inflated Gamma Mixture distribution, ‎it predicts IBNR's‎ ‎loss reserve. ‎‎The model advantage in the IBNR reserve is insurers can predict ‎the number of future claims for each future date. ‎This enables ‎them to change the claim reporting process. The practical applications of our findings are applied against a third party liability (TPL) insurance loss portfolio. Additional information about claim can be considered in the loss reserving ‎model and making the prediction of amount more accurate.