Abstract
AbstractIn retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined‐contribution personal pension plan. The optimal asset allocation is defined so that it minimizes the expected loss of the pensioner as measured by the performance of the pension fund against a benchmark. Two benchmarks are considered: a risk‐free investment and the price of an annuity. The fair‐value income drawdown rate is defined so that the fund performance is a martingale under the objective measure. Annuitization is recommended if the expected fair‐value drawdown rate falls below the annuity rate available at retirement. As an illustration, the annuitization age is calculated for a Gompertz mortality distribution function and a power law loss function.
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