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Income drawdown option with minimum guarantee

Author

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  • Marina Di Giacinto
  • Salvatore Federico
  • Fausto Gozzi
  • Elena Vigna

Abstract

This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement. This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies and on the state variable are present. Due to the difficulty of the task, we consider, as a first step, the basic model of [Gerrard, Haberman & Vigna, 2004], where interim consumption and annuitization time are fixed. We extend their model by adding a no short-selling constraint on the control variable and a final capital requirement constraint on the state variable. This implies, in particular, no ruin. The mathematical problem is naturally formulated as a stochastic control problem with constraints on the control and the state variable, and is approached by the dynamic programming method. We write the non-linear Hamilton-Jacobi-Bellman equation for the problem and transform it into a dual one that is semi-linear, following a well-established duality procedure. In the special relevant case without running cost, we explicitly compute the value function for the problem and give the optimal strategy in feedback form. A numerical application ends the paper and shows the extent of applicability of the model to a DC pension fund in the decumulation phase.

Suggested Citation

  • Marina Di Giacinto & Salvatore Federico & Fausto Gozzi & Elena Vigna, 2012. "Income drawdown option with minimum guarantee," Carlo Alberto Notebooks 272, Collegio Carlo Alberto.
  • Handle: RePEc:cca:wpaper:272
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    References listed on IDEAS

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    Cited by:

    1. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32.
    2. Ayşegül İşcanog̃lu-Çekiç, 2016. "An Optimal Turkish Private Pension Plan with a Guarantee Feature," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-12, June.
    3. Salvatore Federico & Paul Gassiat & Fausto Gozzi, 2015. "Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation," Finance and Stochastics, Springer, vol. 19(2), pages 415-448, April.
    4. Agnieszka Konicz & David Pisinger & Alex Weissensteiner, 2015. "Optimal annuity portfolio under inflation risk," Computational Management Science, Springer, vol. 12(3), pages 461-488, July.

    More about this item

    Keywords

    pension fund; decumulation phase; constrained portfolio; stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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