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Choosing the Optimal Annuitization Time Post Retirement

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Author Info
Russell Gerrard
Bjarne Højgaard
Elena Vigna
Abstract

In the context of decision making for retirees of a defined contribution pension scheme in the de-cumulation phase, we formulate and solve a problem of finding the optimal time of annuitization for a retiree having the possibility of choosing her own investment and consumption strategy. We formulate the problem as a combined stochastic control and optimal stopping problem. As criterion for the optimization we select a loss function that penalizes both the deviance of the running consumption rate from a desired consumption rate and the deviance of the final wealth at the time of annuitization from a desired target. We find closed form solutions for the problem and show the existence of three possible types of solutions depending on the free parameters of the problem. In numerical applications we find the optimal wealth that triggers annuitization, compare it with the desired target and investigate its dependence on both parameters of the financial market and parameters linked to the risk attitude of the retiree. Simulations of the behaviour of the risky asset seem to show that under typical situations optimal annuitization should occur a few years after retirement.

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Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 76.

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Length: 38 pages
Date of creation: 2008
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Handle: RePEc:cca:wpaper:76

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Related research
Keywords: defined contribution pension scheme; de-cumulation phase; stochastic optimal control; optimal annuitization time;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D91 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Consumer Choice; Life Cycle Models and Saving
J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
G23 - Financial Economics - - Financial Institutions and Services - - - Pension Funds; Other Private Financial Institutions

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  16. Massimo Marinacci & Luigi Montrucchio, 2007. "Unique Solutions of Some Recursive Equations in Economic Dynamics," Carlo Alberto Notebooks 46, Collegio Carlo Alberto. [Downloadable!]
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  18. Mario Pagliero, 2007. "The Impact of Potential Labor Supply on Licensing Exam Difficulty in the US Market for Lawyers," Carlo Alberto Notebooks 53, Collegio Carlo Alberto, revised 2009. [Downloadable!]
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