On Optimal Retirement. (June 2014)

• Record Type: Journal Article
• Authors: Ernst, Philip A.; Foster, Dean P.; Shepp, Larry A.
• Is Part Of: Journal of applied probability. Volume 51:Number 2(2014)
• Page Start: 333
• Page End: 345
• Publication Date: 2014-06
• Subjects: Retirement, -- optimal control problem, -- Itô process; 60H10, -- 60J60; 519.2
• DOI: 10.1017/S002190020001127X
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function f and our current net worth X ( t ) for any t, we invest an amount f ( X ( t )) in the market. We need a fortune of M 'superdollars' to retire and want to retire as early as possible. We model our change in net worth over each infinitesimal time interval by the Itô process d X ( t ) = (1 + f ( X ( t )))d t + f ( X ( t ))d W ( t ). We show how to choose the optimal f = f 0 and show that the choice of f 0 is optimal among all nonanticipative investment strategies, not just among Markovian ones.