Income Drawdown Schemes for a Defined‐Contribution Pension Plan

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent 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 minimises 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. Annuitisation is recommended if the expected fair-value drawdown rate falls below the annuity rate available at retirement. As an illustration, the annuitisation age is calculated for a Gompertz mortality distribution function and a power law loss function.

Relative Choice Models for Income Drawdown in a Defined Contribution Pension Scheme

“…However, rather than specify a target fund, they consider a benchmark and measure the performance of the pension fund against this benchmark. In contrast to Gerrard et al (2006), Emms and Haberman (2008) minimize the loss of the pension fund relative to the benchmark; there is no penalty if the pension fund outperforms the benchmark. For their model the income drawdown strategy is prescribed: it is defined so that the fund performance is driftless under the optimal stock allocation strategy.…”

“…Other targets lead to different forms of dynamic strategy, as we shall see in the next section. Emms and Haberman (2008) define fair-value income drawdown such that under an optimal stock allocation the fund performance is a martingale. For an LQ optimization problem, a similar idea is to require that the expected fund size is a fixed percentage below the target for the duration of the drawdown period.…”

“…Following Emms and Haberman (2008) we define the performance of the pension fund measured relative to the target fund F(t) by…”

“…For most pensioners, the fund must be annuitized before age 75. For a thorough introduction to the income drawdown option and other forms of self-annuitization, the reader should refer to the discussion and references in Gerrard et al (2004Gerrard et al ( , 2006, Emms and Haberman (2008), Milevsky (1998), Milevsky and Robinson (2000), Milevsky and Young (2002), and Milevsky et al (2006).…”

An Optimal Turkish Private Pension Plan with a Guarantee Feature

“…For example, Haberman and Sung [2] try to minimize the 'solvency' and 'contribution rate' risks in order to stabilize the pension fund, and Cairns et al try to optimize the terminal utility gained from the pension fund with a stochastic interest rate [3]. Some other examples of the studies that deal with the optimal asset allocations for pension funds can be found in [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. On the other hand, there are limited numbers of studies that consider a target or a guaranteed wealth concept.…”