Abstract
In this article, we are interested in developing an alternative estimation method of the parameters of the hybrid log-Poisson regression model. In our previous paper, we have proposed a hybrid log-Poisson regression model where we have derived the analytical expression of the fuzzy parameters. We found that the hybrid model provide better results than the classical log-Poisson regression model according to the mean square error prediction and the goodness of fit index. However, nowhere we have taken into account the optimal value of h(α-cut) which is of greatest importance in fuzzy regressions literature. In this paper, we provide an alternative estimation method of our hybrid model using a quadratic optimization program and the optimized h-value (α-cut). The expected value of fuzzy number is used as a defuzzification procedure to move from fuzzy values to crisp values. We perform the hybrid model with the alternative estimation we are suggesting on two different numerical data to predict incremental payments in loss reserving. From the mean square error prediction, we prove that the alternative estimation of the new hybrid model with an optimized h-value predicts incremental payments better than the classical log-Poisson regression model as well as the same hybrid model with analytical estimation of parameters. Hence we have optimized the outstanding loss reserves.
Highlights
In [20], there are some experiences where stochastic methods can give unrealistic estimates
We will prove in this paper that the optimized h−value is of the greatest importance because the value of the Mean Square Error Prediction (MSEP) will be very low compared to the MSEP we are getting from the analytical estimation of the hybrid model
We prove that our hybrid model the new estimation method provides best predictions of reserves compared to the classical log-Poisson model according to the MSEP criterion
Summary
In [20], there are some experiences where stochastic methods can give unrealistic estimates. The new model provides better results than the classical logPoisson regression model (according to mean square error prediction (MSEP) and goodness of fit index), we still have a large value of the MSEP. This could be due to the choice of h−value which is important in fuzzy regression framework. Our objective is to come with a new estimation method of fuzzy parameters in the hybrid log-Poisson model where the optimized h−value will be taken into account. We prove that our hybrid model the new estimation method provides best predictions of reserves compared to the classical log-Poisson model according to the MSEP criterion
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