Document Zbl 1427.91225

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Denuit</span> and <span class="zbmathjax-textit">J. Dhaene</span> [Insur. Math. Econ. 51, No. 2, 265–270 (2012; <a href="/1284.60043">Zbl 1284.60043</a>)] proposed the conditional mean risk sharing rule to allocate the total risk among participants to an insurance pool. This paper relates the conditional mean risk sharing rule to the size-biased transform when pooled risks are independent. A representation formula is first derived for the conditional expectation of an individual risk given the aggregate loss. This formula is then exploited to obtain explicit expressions for the contributions to the pool when losses are modeled by compound Poisson sums, compound negative binomial sums, and compound binomial sums, to which Panjer recursion applies. Simple formulas are obtained when claim severities are homogeneous. A couple of applications are considered: first, to a peer-to-peer insurance scheme where participants share the first layer of their respective risks while the higher layer is ceded to a (re)insurer; second, to survivor credits to be shared among surviving participants in tontine schemes.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7135573">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7135573">Cited in <strong>21</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%3A62P05" title="MSC2020">62P05</a> </td> <td class="space"> Applications of statistics to actuarial sciences and financial mathematics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconditional+expectation">conditional expectation</a>; <a href="/?q=ut%3Arisk+pooling">risk pooling</a>; <a href="/?q=ut%3Arisk+measures">risk measures</a>; <a href="/?q=ut%3Acompound+distributions">compound distributions</a>; <a href="/?q=ut%3APanjer+family+of+distributions">Panjer family of distributions</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1284.60043">Zbl 1284.60043</a></div> <div class="software"> <h3>Software:</h3><a href="/software/6079">actuar</a></div>  <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;">  </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">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1427.91225" data-ciurl="/ci/07135573" data-biburl="/bibtex/07135573.bib" data-amsurl="/amsrefs/07135573.bib" data-xmlurl="/xml/07135573.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07135573.pdf" title="Zbl 1427.91225 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/10.1017/asb.2019.24" aria-label="DOI for “Size-biased transform and conditional mean risk sharing, with application to p2p insurance and tontines”" title="10.1017/asb.2019.24">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://dial.uclouvain.be/pr/boreal/fr/object/boreal%3A215115/datastream/PDF_01/view" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Arratia, R., Goldstein, L., and Kochman, F. 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