Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model</title> <meta name="description" content="Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model"> <meta name="keywords" content="DC pension fund, modified constant elasticity of variance, optimal investment strategies, voluntary contribution, administrative charges."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <meta name="citation_title" content="Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model"> <meta name="citation_author" content="Amadi Ugwulo Chinyere"> <meta name="citation_author" content="Lewis D. Gbarayorks"> <meta name="citation_author" content="Emem N. H. Inamete"> <meta name="citation_publication_date" content="2022/12/15"> <meta name="citation_journal_title" content="International Journal of Physical and Mathematical Sciences"> <meta name="citation_volume" content="16"> <meta name="citation_issue" content="12"> <meta name="citation_firstpage" content="120"> <meta name="citation_lastpage" content="125"> <meta name="citation_pdf_url" content="https://publications.waset.org/10012839/pdf"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value=""> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 33093</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Amadi%20Ugwulo%20Chinyere">Amadi Ugwulo Chinyere</a>, <a href="https://publications.waset.org/search?q=Lewis%20D.%20Gbarayorks"> Lewis D. Gbarayorks</a>, <a href="https://publications.waset.org/search?q=Emem%20N.%20H.%20Inamete"> Emem N. H. Inamete</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the mandatory contribution, additional voluntary contribution (AVC) and administrative charges are merged together to determine the optimal investment strategy (OIS) for a pension plan member (PPM) in a defined contribution (DC) pension scheme under the modified constant elasticity of variance (M-CEV) model. We assume that the voluntary contribution is a stochastic process and a portfolio consisting of one risk free asset and one risky asset modeled by the M-CEV model is considered. Also, a stochastic differential equation consisting of PPM’s monthly contributions, voluntary contributions and administrative charges is obtained. More so, an optimization problem in the form of Hamilton Jacobi Bellman equation which is a nonlinear partial differential equation is obtained. Using power transformation and change of variables method, an explicit solution of the OIS and the value function are obtained under constant absolute risk averse (CARA). Furthermore, numerical simulations on the impact of some sensitive parameters on OIS were discussed extensively. Finally, our result generalizes some existing result in the literature.</p> <iframe src="https://publications.waset.org/10012839.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=DC%20pension%20fund" title="DC pension fund">DC pension fund</a>, <a href="https://publications.waset.org/search?q=modified%20constant%20elasticity%20of%20variance" title=" modified constant elasticity of variance"> modified constant elasticity of variance</a>, <a href="https://publications.waset.org/search?q=optimal%20investment%20strategies" title=" optimal investment strategies"> optimal investment strategies</a>, <a href="https://publications.waset.org/search?q=voluntary%20contribution" title=" voluntary contribution"> voluntary contribution</a>, <a href="https://publications.waset.org/search?q=administrative%20charges." title=" administrative charges."> administrative charges.</a> </p> <a href="https://publications.waset.org/10012839/modelling-an-investment-portfolio-with-mandatory-and-voluntary-contributions-under-m-cev-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10012839/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10012839/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10012839/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10012839/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10012839/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10012839/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10012839/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10012839/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10012839/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10012839/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10012839.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">373</span> </span> <p class="card-text"><strong>References:</strong></p> <br>[1] R. 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Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model