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- Title
ON OPTIMAL RETIREMENT.
- Authors
ERNST, PHILIP A.; FOSTER, DEAN P.; SHEPP, LARRY A.
- 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 dX(t) = (1 + f(X(t))) dt + f(X(t)) d W(t). We show how to choose the optimal f = f0 and show that the choice of f0 is optimal among all nonanticipative investment strategies, not just among Markovian ones.
- Subjects
OPTIMAL control theory; INFINITESIMAL geometry; MARKOV spectrum; CONTROL theory (Engineering); INVESTMENTS
- Publication
Journal of Applied Probability, 2014, Vol 51, Issue 2, p333
- ISSN
0021-9002
- Publication type
Article
- DOI
10.1239/jap/1402578628