Evaluation Of Individual Loss Reserving Based On Generalized Linear Model

Liability reserve refers to the insurance company's future responsibility and deal with the outstanding claims, deposited a kind of capital from the insurance premium income, with uncertainty, future-oriented, estimability. Studies have put forward a lot of uncertainty and randomness method to estimate the outstanding claims reserve. The traditional liability reserve evaluation methods are based on aggregate data, for example Chain ladder method(CL method), BF method and some stochastic model. It is easy to calculate using the aggregate data to evaluate the liability reserve, but the aggregated data which is sum of all individuals within a certain time, is bound to loss useful information which individual data contains, and may lead to inaccurate for predicting the outstanding claims reserve. In this paper, we construct generalized linear model on estimating the outstanding claims reserve based on individual data. Firstly, the individual claim amount is assumed to be exponential distribution family, and a claim is paid only once at its settlement,under the assumption of report number is known, and the delay of payment is random, we studied the RBNS reserving. Secondly, we studied the IBNR reserving, due to failing to report the accident in time, we assume both the number of accidents and the delay of report are random, then get the estimation of IBNR. Finally, the total liability reserving is studied, under the total reserve model, all of the the delays of report and settlement are assumed random, and we construct the generalized linear model, then get the expression and estimation of the liability reserve. Also we estimate the parameter in the model, and the large sample character of the parameter estimation are studied. At last, simulation studies show that the individual method which is based on the generalized linear model is obviously better than the chain ladder method.