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Optimal Asset Allocation For Dc Pension Decumulation With A Variable Spending Rule

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  • Forsyth, Peter A.
  • Vetzal, Kenneth R.
  • Westmacott, Graham

Abstract

We determine the optimal asset allocation to bonds and stocks using an annually recalculated virtual annuity (ARVA) spending rule for DC pension plan decumulation. Our objective function minimizes downside withdrawal variability for a given fixed value of total expected withdrawals. The optimal asset allocation is found using optimal stochastic control methods. We formulate the strategy as a solution to a Hamilton–Jacobi–Bellman (HJB) Partial Integro Differential Equation (PIDE). We impose realistic constraints on the controls (no-shorting, no-leverage, discrete rebalancing) and solve the HJB PIDEs numerically. Compared to a fixed-weight strategy which has the same expected total withdrawals, the optimal strategy has a much smaller average allocation to stocks and tends to de-risk rapidly over time. This conclusion holds in the case of a parametric model based on historical data and also in a bootstrapped market based on the historical data.

Suggested Citation

  • Forsyth, Peter A. & Vetzal, Kenneth R. & Westmacott, Graham, 2020. "Optimal Asset Allocation For Dc Pension Decumulation With A Variable Spending Rule," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 419-447, May.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:2:p:419-447_4
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    Cited by:

    1. Pengyu Wei & Charles Yang, 2023. "Optimal investment for defined-contribution pension plans under money illusion," Review of Quantitative Finance and Accounting, Springer, vol. 61(2), pages 729-753, August.
    2. Peter A. Forsyth & Kenneth R. Vetzal & Graham Westmacott, 2021. "Optimal control of the decumulation of a retirement portfolio with variable spending and dynamic asset allocation," Papers 2101.02760, arXiv.org.
    3. Peter A. Forsyth, 2020. "A Stochastic Control Approach to Defined Contribution Plan Decumulation: "The Nastiest, Hardest Problem in Finance"," Papers 2008.06598, arXiv.org.
    4. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.
    5. Forsyth, Peter A., 2020. "Optimal dynamic asset allocation for DC plan accumulation/decumulation: Ambition-CVAR," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 230-245.

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