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J. Oper. Res.</a> <a href="/?q=in%3A443687" title="Articles in this Issue">282, No. 1, 345-362 (2020)</a>. </div> <div class="abstract">Summary: This paper studies the optimal dynamic reinsurance policy for an insurance company whose surplus is modeled by the diffusion approximation of the classical Cramér-Lundberg model. We assume the reinsurance premium is calculated according to a proposed mean-CVaR premium principle which generalizes Denneberg’s absolute deviation principle and expected value principle. Moreover, we require that both ceded loss and retention functions are non-decreasing to rule out moral hazard. Under the objective of minimizing the ruin probability, we obtain the optimal reinsurance policy explicitly and we denote the resulting treaty as the dual excess-of-loss reinsurance. This form of the optimal treaty is new to the literature and lends support to the fact that reinsurance contracts in practice often involve layers. It also demonstrates that reinsurance treaties such as the proportional and the standard excess-of-loss, which are typically found to be optimal in the dynamic reinsurance model, need not be optimal when we consider a more general optimization model. We also consider other generalizations including (i) allowing the insurer to manage its business through both reinsurance and investment; and (ii) \(N\)-piecewise mean-CVaR premium principle. In the former case, we not only show that the dual excess-of-loss reinsurance policy remains optimal, but also demonstrate that investing in stock can further enhance insurer’s financial stability with lower ruin probability. For the latter case, we establish that the optimal reinsurance treaty can have at most \(N\) layers, which is also more consistent with practice.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7148584">Cited in <strong>24</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A91G05" title="MSC2020">91G05</a> </td> <td class="space"> Actuarial mathematics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A91G10" title="MSC2020">91G10</a> </td> <td class="space"> Portfolio theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Arisk+management">risk management</a>; <a href="/?q=ut%3Areinsurance">reinsurance</a>; <a href="/?q=ut%3Amean-CVaR">mean-CVaR</a>; <a href="/?q=ut%3Aruin+probability">ruin probability</a>; <a href="/?q=ut%3Amoral+hazard">moral hazard</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1431.91344" data-ciurl="/ci/07148584" data-biburl="/bibtex/07148584.bib" data-amsurl="/amsrefs/07148584.bib" data-xmlurl="/xml/07148584.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07148584.pdf" title="Zbl 1431.91344 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.ejor.2019.08.053" aria-label="DOI for “Optimal dynamic reinsurance policies under a generalized Denneberg's absolute deviation principle”" title="10.1016/j.ejor.2019.08.053">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Albrecher, H.; Beirlant, J.; Teugels, J. 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