{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T22:47:40Z","timestamp":1787870860006,"version":"build-2784847793"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Finan. Math."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential L\u00e9vy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an It\u00f4 market, we employ the concept of market time, which is a clock that runs according to the underlying market growth. We show the optimality of the growth-optimal portfolio for minimizing the expected market time to reach any wealth level. This reveals a general definition of market time which can be useful from an investor's point of view. We utilize this last definition to extend the previous results in a general semimartingale setting.<\/jats:p>","DOI":"10.1137\/080741124","type":"journal-article","created":{"date-parts":[[2010,2,23]],"date-time":"2010-02-23T16:32:08Z","timestamp":1266942728000},"page":"16-29","source":"Crossref","is-referenced-by-count":14,"title":["Minimizing the Expected Market Time to Reach a Certain Wealth Level"],"prefix":"10.1137","volume":"1","author":[{"given":"Constantinos","family":"Kardaras","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eckhard","family":"Platen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,1,21]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176991793"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"D. C. Aucamp,\n                      An investment strategy with overshoot rebates which minimizes the time to attain a specified goal\n                      , Management Sci., 23 (1976\/77), pp. 1234\u20131241.","DOI":"10.1287\/mnsc.23.11.1234"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013535"},{"key":"R4","unstructured":"F. Black,\n                      Studies of stock price volatility changes\n                      , in Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, Berkeley, CA, 1976, pp. 177\u2013181."},{"key":"R5","doi-asserted-by":"crossref","unstructured":"L. Breiman,\n                      Optimal gambling systems for favorable games\n                      , in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probablility, Vol. I, University of California Press, Berkeley, CA, 1961, pp. 65\u201378.","DOI":"10.21236\/AD0402290"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1029955147"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1080\/07362990600870488"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177004600"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/s007800050062"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0325012"},{"key":"R11","unstructured":"D. Heath and W. Sudderth,\n                      Continuous-Time Portfolio Management: Minimizing the Expected Time to Reach a Goal\n                      , manuscript, 1984."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-007-0047-3"},{"key":"R13","unstructured":"I. Karatzas and S. E. Shreve,\n                      Brownian Motion and Stochastic Calculus\n                      , 2nd ed., Grad. Texts in Math. 113, Springer-Verlag, New York, 1991."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2009.00363.x"},{"key":"R15","unstructured":"C. Kardaras and E. Platen,\n                      On the Semimartingale Property of Discounted Asset-Price Processes\n                      , preprint, http:\/\/arxiv.org\/abs\/0803.1890."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1956.tb03809.x"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(90)90012-O"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2006.00265.x"},{"key":"R19","unstructured":"K.I. Sato,\n                      L\u00e9vy Processes and Infinitely Divisible Distributions\n                      , Cambridge Stud. Adv. Math. 68, Cambridge University Press, Cambridge, UK, 1999."}],"container-title":["SIAM Journal on Financial Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080741124","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:29:18Z","timestamp":1787322558000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080741124"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080741124"],"URL":"https:\/\/doi.org\/10.1137\/080741124","relation":{},"ISSN":["1945-497X"],"issn-type":[{"value":"1945-497X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}