The income drawdown option gives a retiring member of a defined contribution pension scheme the opportunity to defer the purchase of an annuity and instead to manage the investment of the accumulated fund for a period before finally annuitising. During the period before the purchase of the annuity the scheme member will draw an income from the fund, which may vary in accordance with the requirements set by the scheme's rules or the legislation. In some countries which permit this scheme, such as the UK, there are restrictions on the age by which annuitization must occur and on the amount of income which can be drawn from the fund. We investigate a scenario in which the retiring member specifies in advance the level of income which she/he considers desirable and manages the investment and consumption in such a way as to minimize the expected discounted loss over the infinite horizon, where the loss function used is the square of the difference between the actual income and the ideal. The analysis is performed first in the case where mortality is ignored, so that the annuity is in effect a perpetuity, then in the case where mortality plays a role and where in addition we consider the possibility that the retiree may derive some utility from being able to bequeath the contents of the fund in the event of death before annuitization. In both cases, the techniques of stochastic optimal control are employed to derive an explicit optimal strategy in the absence of restrictions. The effect of imposing restrictions --- on the income drawn and on the proportion of the fund invested in a risky asset --- is investigated and some indications are given on the methodology to be followed when tackling the problem, but no explicit solution is found. Numerical examples provided by simulating the behaviour of the financial market illustrate the practical effect of the application of the optimal rules provided by the theoretical model. We emphasize the feasibility of the optimal choices, in terms of certain reasonable restrictions (e.g. consumption should be non negative and short selling of any asset not allowed). Other relevant issues are investigated, for example the probability of ruin and how the weight given to the bequest motive affects optimal choices.
The income drawdown option: quadratic loss
VIGNA, Elena
2004-01-01
Abstract
The income drawdown option gives a retiring member of a defined contribution pension scheme the opportunity to defer the purchase of an annuity and instead to manage the investment of the accumulated fund for a period before finally annuitising. During the period before the purchase of the annuity the scheme member will draw an income from the fund, which may vary in accordance with the requirements set by the scheme's rules or the legislation. In some countries which permit this scheme, such as the UK, there are restrictions on the age by which annuitization must occur and on the amount of income which can be drawn from the fund. We investigate a scenario in which the retiring member specifies in advance the level of income which she/he considers desirable and manages the investment and consumption in such a way as to minimize the expected discounted loss over the infinite horizon, where the loss function used is the square of the difference between the actual income and the ideal. The analysis is performed first in the case where mortality is ignored, so that the annuity is in effect a perpetuity, then in the case where mortality plays a role and where in addition we consider the possibility that the retiree may derive some utility from being able to bequeath the contents of the fund in the event of death before annuitization. In both cases, the techniques of stochastic optimal control are employed to derive an explicit optimal strategy in the absence of restrictions. The effect of imposing restrictions --- on the income drawn and on the proportion of the fund invested in a risky asset --- is investigated and some indications are given on the methodology to be followed when tackling the problem, but no explicit solution is found. Numerical examples provided by simulating the behaviour of the financial market illustrate the practical effect of the application of the optimal rules provided by the theoretical model. We emphasize the feasibility of the optimal choices, in terms of certain reasonable restrictions (e.g. consumption should be non negative and short selling of any asset not allowed). Other relevant issues are investigated, for example the probability of ruin and how the weight given to the bequest motive affects optimal choices.
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