{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:39:01Z","timestamp":1787323141076,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic control problem is solved using dynamic programming arguments. We show by analytical methods that the associated Hamilton\u2013Jacobi\u2013Bellman equation has a smooth solution and then obtain the existence and representation of the optimal control in feedback form using verification arguments.<\/jats:p>","DOI":"10.1137\/100790884","type":"journal-article","created":{"date-parts":[[2012,3,27]],"date-time":"2012-03-27T19:00:19Z","timestamp":1332874819000},"page":"790-819","source":"Crossref","is-referenced-by-count":23,"title":["Optimal Investment with High-watermark Performance Fee"],"prefix":"10.1137","volume":"50","author":[{"given":"Karel","family":"Jane\u010dek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihai","family":"S\u00eerbu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,3,27]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.2009.01499.x"},{"key":"R2","unstructured":"J. Aragon and J. Qian,\n                      The Role of High-Watermarks in Hedge-Fund Compensation\n                      , preprint, 2007."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"J. Cvitanic and I. Karatzas,\n                      On Portfolio Optimization under Drawdown Constraints\n                      , IMA Lecture Notes in Math. Appl. 65, 1995, pp. 77\u201388.","DOI":"10.1007\/978-1-4757-2435-6_3"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1287\/moor.15.4.676"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-008-0066-8"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1111\/1540-6261.00581"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1993.tb00044.x"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"P. Guasoni and J. Obloj,\n                      The Incentives of Hedge Fund Fees and High-Water-Marks\n                      , preprint, 2009.","DOI":"10.2139\/ssrn.1570411"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-003-0113-4"},{"key":"R11","unstructured":"K. Jane\u010dek and S. Shreve,\n                      Futures trading with transaction costs\n                      , Illinois J. Math., to appear."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.2307\/1926560"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(71)90038-X"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.2008.01427.x"},{"key":"R15","unstructured":"H. Roche,\n                      Optimal Consumption and Investment Strategies Under Wealth Racheting\n                      , preprint 2006."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177004966"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00034"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100790884","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:44:17Z","timestamp":1787319857000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100790884"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1137\/100790884"],"URL":"https:\/\/doi.org\/10.1137\/100790884","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}