The Bayesian Premium Under Entropy Loss

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Loss</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Farouk%20Metiri">Farouk Metiri</a>, <a href="https://publications.waset.org/abstracts/search?q=Halim%20Zeghdoudi"> Halim Zeghdoudi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Riad%20Remita"> Mohamed Riad Remita</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Credibility theory is an experience rating technique in actuarial science which can be seen as one of quantitative tools that allows the insurers to perform experience rating, that is, to adjust future premiums based on past experiences. It is used usually in automobile insurance, worker's compensation premium, and IBNR (incurred but not reported claims to the insurer) where credibility theory can be used to estimate the claim size amount. In this study, we focused on a popular tool in credibility theory which is the Bayesian premium estimator, considering Lindley distribution as a claim distribution. We derive this estimator under entropy loss which is asymmetric and squared error loss which is a symmetric loss function with informative and non-informative priors. In a purely Bayesian setting, the prior distribution represents the insurer鈥檚 prior belief about the insured鈥檚 risk level after collection of the insured鈥檚 data at the end of the period. However, the explicit form of the Bayesian premium in the case when the prior is not a member of the exponential family could be quite difficult to obtain as it involves a number of integrations which are not analytically solvable. The paper finds a solution to this problem by deriving this estimator using numerical approximation (Lindley approximation) which is one of the suitable approximation methods for solving such problems, it approaches the ratio of the integrals as a whole and produces a single numerical result. Simulation study using Monte Carlo method is then performed to evaluate this estimator and mean squared error technique is made to compare the Bayesian premium estimator under the above loss functions. <iframe src="https://publications.waset.org/abstracts/47704.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bayesian%20estimator" title="bayesian estimator">bayesian estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=credibility%20theory" title=" credibility theory"> credibility theory</a>, <a href="https://publications.waset.org/abstracts/search?q=entropy%20loss" title=" entropy loss"> entropy loss</a>, <a href="https://publications.waset.org/abstracts/search?q=monte%20carlo%20simulation" title=" monte carlo simulation"> monte carlo simulation</a> </p> <a href="https://publications.waset.org/abstracts/47704/the-bayesian-premium-under-entropy-loss" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47704.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">334</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> 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The Bayesian Premium Under Entropy Loss