{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:41:25Z","timestamp":1682502085725},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function <jats:italic>f<\/jats:italic> and our current net worth <jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>) for any <jats:italic>t<\/jats:italic>, we invest an amount <jats:italic>f<\/jats:italic>(<jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>)) in the market. We need a fortune of <jats:italic>M<\/jats:italic> \u2018superdollars\u2019 to retire and want to retire as early as possible. We model our change in net worth over each infinitesimal time interval by the It\u00f4 process d<jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>) = (1 + <jats:italic>f<\/jats:italic>(<jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>)))d<jats:italic>t<\/jats:italic> + <jats:italic>f<\/jats:italic>(<jats:italic>X<\/jats:italic>(<jats:italic>t<\/jats:italic>))d<jats:italic>W<\/jats:italic>(<jats:italic>t<\/jats:italic>). We show how to choose the optimal <jats:italic>f<\/jats:italic> = <jats:italic>f<\/jats:italic>\n               <jats:sub>0<\/jats:sub> and show that the choice of <jats:italic>f<\/jats:italic>\n               <jats:sub>0<\/jats:sub> is optimal among all nonanticipative investment strategies, not just among Markovian ones.<\/jats:p>","DOI":"10.1017\/s002190020001127x","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:51:10Z","timestamp":1459263070000},"page":"333-345","source":"Crossref","is-referenced-by-count":3,"title":["On Optimal Retirement"],"prefix":"10.1017","volume":"51","author":[{"given":"Philip A.","family":"Ernst","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dean P.","family":"Foster","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Larry A.","family":"Shepp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S002190020001127X_ref2","first-page":"1","volume":"1","year":"1991","journal-title":"Math. Finance"},{"key":"S002190020001127X_ref1","doi-asserted-by":"publisher","DOI":"10.1086\/260062"},{"key":"S002190020001127X_ref9","volume-title":"Continuous-Time Finance","year":"1992"},{"key":"S002190020001127X_ref4","volume-title":"Diffusion Processes and Their Sample Paths","year":"1965"},{"key":"S002190020001127X_ref7","volume-title":"Stochastic Integrals","year":"1969"},{"key":"S002190020001127X_ref6","volume-title":"A Second Course in Stochastic Processes","year":"1981"},{"key":"S002190020001127X_ref5","volume-title":"Brownian Motion and Stochastic Calculus","year":"1991"},{"key":"S002190020001127X_ref8","doi-asserted-by":"publisher","DOI":"10.2307\/1926560"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002190020001127X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T09:04:51Z","timestamp":1682499891000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002190020001127X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":8,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["S002190020001127X"],"URL":"https:\/\/doi.org\/10.1017\/s002190020001127x","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}