{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T07:02:34Z","timestamp":1763017354427,"version":"3.37.3"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Humanities and Social Science Research Youth Foundation of Ministry of Education","award":["11YJC790006","20100821"],"award-info":[{"award-number":["11YJC790006","20100821"]}]},{"name":"Higher School Science and Technology Development Foundation of Tianjin","award":["11YJC790006","20100821"],"award-info":[{"award-number":["11YJC790006","20100821"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying variable change technique.<\/jats:p>","DOI":"10.1155\/2013\/348059","type":"journal-article","created":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T16:01:54Z","timestamp":1383840114000},"page":"1-8","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3452-9477","authenticated-orcid":true,"given":"Hao","family":"Chang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi-min","family":"Rong","sequence":"additional","affiliation":[{"name":"School of Science, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"1-2","key":"1","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0304-405X(76)90023-4","volume":"3","year":"1976","journal-title":"Journal of Financial Economics"},{"issue":"3","key":"2","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1086\/260062","volume":"81","year":"1973","journal-title":"Journal of Political Economy"},{"issue":"1","key":"3","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.1540-6261.1989.tb02414.x","volume":"44","year":"1989","journal-title":"Journal of Finance"},{"issue":"2","key":"4","doi-asserted-by":"crossref","first-page":"241","DOI":"10.2307\/2676280","volume":"34","year":"1999","journal-title":"Journal of Financial and Quantitative Analysis"},{"issue":"7","key":"5","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1287\/mnsc.47.7.949.9804","volume":"47","year":"2001","journal-title":"Management Science"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2006.04.007"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2009.02.006"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2010.01.009"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.2307\/2937799"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.16.4.802"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1006\/jeth.1997.2285"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1889(99)00089-5"},{"issue":"1","key":"12","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1137\/S0363012991218827","volume":"32","year":"1994","journal-title":"SIAM Journal on Control and Optimization"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s002450010003"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900378504"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2006.03.006"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2007.10.014"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2009.01.005"},{"year":"1968","key":"20"},{"key":"9","series-title":"NATO Science Series II","first-page":"255","volume-title":"Optimal investment problems and volatility homogenization approximations","volume":"75","year":"2002"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/348059.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/348059.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/348059.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T21:35:42Z","timestamp":1498080942000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/348059\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":20,"alternative-id":["348059","348059"],"URL":"https:\/\/doi.org\/10.1155\/2013\/348059","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}