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On Optimal Retirement

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  19 February 2016

Philip A. Ernst ,
Dean P. Foster  and
Larry A. Shepp
Philip A. Ernst*
Affiliation:
University of Pennsylvania
Dean P. Foster*
Affiliation:
University of Pennsylvania
Larry A. Shepp*
Affiliation:
University of Pennsylvania
*
∗ Postal address: The Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, PA 19104, USA.
∗ Postal address: The Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, PA 19104, USA.
∗ Postal address: The Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, PA 19104, USA.
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Abstract

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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))dW(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.

Keywords

Retirementoptimal control problemItô process

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 60J60: Diffusion processes
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 333 - 345
Copyright
© Applied Probability Trust 

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