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Theophilus"> <meta name="citation_author" content="Prince Benjamin"> <meta name="citation_publication_date" content="2024/09/06"> <meta name="citation_journal_title" content="International Journal of Mathematical and Computational Sciences"> <meta name="citation_volume" content="18"> <meta name="citation_issue" content="9"> <meta name="citation_firstpage" content="102"> <meta name="citation_lastpage" content="109"> <meta name="citation_pdf_url" content="https://publications.waset.org/10013803/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">Application of Legendre Transformation to Portfolio Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Peter%20Benneth">Peter Benneth</a>, <a href="https://publications.waset.org/search?q=Tsaroh%20N.%20Theophilus"> Tsaroh N. Theophilus</a>, <a href="https://publications.waset.org/search?q=Prince%20Benjamin"> Prince Benjamin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This research work aims at studying the application of Legendre Transformation Method (LTM) to Hamilton Jacobi Bellman (HJB) equation which is an example of optimal control problem. We discuss the steps involved in modelling the HJB equation as it relates to mathematical finance by applying the Ito’s lemma and maximum principle theorem. By applying the LTM and dual theory, the resultant HJB equation is transformed to a linear Partial Differential Equation (PDE). Also, the Optimal Investment Strategy (OIS) and the optimal value function were obtained under the exponential utility function. Furthermore, some numerical results were also presented with observations that the OIS under exponential utility is directly proportional to the appreciation rate of the risky asset and inversely proportional to the instantaneous volatility, predetermined interest rate, risk averse coefficient. Finally, it was observed that the optimal fund size is an increasing function of the risk free interest rate. This result is consistent with some existing results.</p> <iframe src="https://publications.waset.org/10013803.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Legendre%20transformation%20method" title="Legendre transformation method">Legendre transformation method</a>, <a href="https://publications.waset.org/search?q=Optimal%20investment%20strategy" title=" Optimal investment strategy"> Optimal investment strategy</a>, <a href="https://publications.waset.org/search?q=Ito%E2%80%99s%20lemma" title=" Ito’s lemma"> Ito’s lemma</a>, <a href="https://publications.waset.org/search?q=Hamilton%20Jacobi%20Bellman%20equation" title=" Hamilton Jacobi Bellman equation"> Hamilton Jacobi Bellman equation</a>, <a href="https://publications.waset.org/search?q=Geometric%20Brownian%20motion" title=" Geometric Brownian motion"> Geometric Brownian motion</a>, <a href="https://publications.waset.org/search?q=financial%20market." title=" financial market."> financial market.</a> </p> <a href="https://publications.waset.org/10013803/application-of-legendre-transformation-to-portfolio-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10013803/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10013803/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10013803/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10013803/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10013803/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10013803/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10013803/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10013803/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10013803/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10013803/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10013803.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">67</span> </span> <p class="card-text"><strong>References:</strong></p> <br>[1] Rao, K. 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