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Optimal control of the decumulation of a retirement portfolio with variable spending and dynamic asset allocation. (English) Zbl 1476.65280

Summary: We extend the Annually Recalculated Virtual Annuity (ARVA) spending rule for retirement savings decumulation [M. B. Waring and L. B. Siegel, “The only spending rule article you will ever need”, Financ. Anal. J. 71, No. 1, 91–107 (2015; doi:10.2469/faj.v71.n1.2)] to include a cap and a floor on withdrawals. With a minimum withdrawal constraint, the ARVA strategy runs the risk of depleting the investment portfolio. We determine the dynamic asset allocation strategy which maximizes a weighted combination of expected total withdrawals (EW) and expected shortfall (ES), defined as the average of the worst 5% of the outcomes of real terminal wealth. We compare the performance of our dynamic strategy to simpler alternatives which maintain constant asset allocation weights over time accompanied by either our same modified ARVA spending rule or withdrawals that are constant over time in real terms. Tests are carried out using both a parametric model of historical asset returns as well as bootstrap resampling of historical data. Consistent with previous literature that has used different measures of reward and risk than EW and ES, we find that allowing some variability in withdrawals leads to large improvements in efficiency. However, unlike the prior literature, we also demonstrate that further significant enhancements are possible through incorporating a dynamic asset allocation strategy rather than simply keeping asset allocation weights constant throughout retirement.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35Q93 PDEs in connection with control and optimization
91G05 Actuarial mathematics
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