{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:46:17Z","timestamp":1760233577322,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is generally known that Lie symmetries of differential equations can lead to a reduction of the governing equation(s), lead to exact solutions of these equations and, in the best case scenario, lead to a linearization of the original equation. In this paper, we consider a model from optimal investment theory where we show the governing equation possesses an extensive contact symmetry and, through this, we show it is linearizable. Several exact solutions are provided including a solution to a particular terminal value problem.<\/jats:p>","DOI":"10.3390\/sym13020217","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T09:03:45Z","timestamp":1611824625000},"page":"217","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Contact Symmetries of a Model in Optimal Investment Theory"],"prefix":"10.3390","volume":"13","author":[{"given":"Daniel J.","family":"Arrigo","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Central Arkansas, Conway, AR 72035, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph A.","family":"Van de Grift","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Central Arkansas, Conway, AR 72035, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Arrigo, D.J. 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Symmetry Analysis of Differential Equations: An Introduction, John Wiley & Sons, Inc."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bluman, G., and Kumei, S. (1989). Symmetries and Differential Equations, Springer.","DOI":"10.1007\/978-1-4757-4307-4"},{"key":"ref_8","unstructured":"Bluman, G., and Anco, S.C. (2002). Symmetry and Integration Methods for Differential Equations, Springer."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bordag, L.A. (2015). Geometrical Properties of Differential Equations. Applications of the Lie Group Analysis in Financial Mathematics, World Scientific.","DOI":"10.1142\/9549"},{"key":"ref_10","unstructured":"Cantwell, B.J. (2002). Introduction to Symmetry Analysis, Cambridge Texts in Applied Mathematics."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cherniha, R., Mykola, S., and Pliukhin, O. (2018). 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Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1137\/0142079","article-title":"When nonlinear differential equations are equivalent to linear differential equations","volume":"42","author":"Bluman","year":"1982","journal-title":"SIAM J. Appl. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"141","DOI":"10.2307\/3003143","article-title":"Theory of Rational Option Pricing","volume":"4","author":"Merton","year":"1973","journal-title":"Bell J. Econ. Manag. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1086\/260062","article-title":"The pricing of Options and Corporate Liabilities","volume":"81","author":"Black","year":"1973","journal-title":"J. Political Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1023\/A:1008304132308","article-title":"Lie Symmetry Analysis of Differential Equations in Finance","volume":"17","author":"Gazizov","year":"1998","journal-title":"Nonlinear Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1006\/jmaa.1999.6331","article-title":"All solutions of standard symmetric linear partial differential equations have a classical Lie symmetry","volume":"234","author":"Broadbridge","year":"1999","journal-title":"J. Math. Anal. Appl."},{"key":"ref_20","unstructured":"Dimov, I., Dimova, S., and Kolkovska, N. (2010). A numerical study of a parabolic Monge-Ampere equation in mathematical finance. Numerical Methods and Applications. Lecture Notes in Computer Science, Springer."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/217\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:16:44Z","timestamp":1760159804000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/2\/217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,28]]},"references-count":20,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["sym13020217"],"URL":"https:\/\/doi.org\/10.3390\/sym13020217","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,1,28]]}}}