We base our analysis on an investor, usually a retiree, endowed with a certain amount of wealth W, who considers both his own consumption needs (fixed periodic withdrawals) and the requirement of his heirs (defined bequest). For this purpose he pursues the following investment strategy. The part F is invested in a set of investment funds with the target to achieve an accumulated wealth at the end of a certain time horizon of at least the original amount of wealth W (or the fraction (1-h)W), measured in real terms. As certain investment risks are implied, we allow for the probability of falling short of the target and implement it into our model as a risk control parameter. The remaining part MM of the original wealth is invested in money market funds in order to avoid additional investment risks and deliver fixed periodic withdrawals until the end of the respective time horizon. The optimal investment strategy is the investment fund allocation that satisfies the probability of shortfall and minimizes F, while maximizing the fixed periodic withdrawals. We outline this investment problem in a mathematical model and illustrate the solution for a reasonable choice of empirical parameters.
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