Abstract
We consider the Gamma Lindley distribution (GaL) as the conditional distribution of (X|θ,γ), we focus on the estimation of the Bayesian premium under squared error loss function (symmetric) and linear-exponential (Linex) loss function (asymmetric), using informative priors (the Gamma prior). Because of its difficulty and non-linearity, we use a numerical approximation for computing the Bayesian premium. Finally, a simulation and comparative study with varying sample sizes are given.
Highlights
The credibility theory is one of the important quantitative techniques in actuarial science that allow insurance companies to perform an experience assessment
In practice, the real loss function is often not symmetric. It may be noted in the Gamma Lindley distribution that when θ increases μ(θ,γ), decreases and the Bayesian premium estimator tends to μ(θ,γ)
It has been observed that the Bayesian premium estimator that gives the smallest average absolute error over all the other Bayesian premium estimators in majority of the cases is Bayesian premium estimator under the generalized prior with Linex loss function especially when the loss parameter is less than zero i.e., (a = −0.5)
Summary
The credibility theory is one of the important quantitative techniques in actuarial science that allow insurance companies to perform an experience assessment (adjusting future premiums based on past experience). We evaluate the Bayesian premium estimators under the above loss functions; a simulation using Monte Carlo method and mean squared error technique are given. This section considers estimation of the Bayesian premium pB based on the above-mentioned priors and loss functions.
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