ABSTRACT Endowment funds and similar institutions aim to generate a benefit stream of unlimited duration on the basis of an initially donated capital. Towards this purpose, responsible trustees need to design a spending policy as well as an investment policy. A combined spending and investment policy is said to be efficient if the total net present value of benefits that are paid according to the policy is equal to the initial capital, and inefficient if the total net present value is less than that. For several strategies, analytical expressions are given for the total net present value of benefits under the Black-Scholes assumptions. One of the strategies considered is the combination of a fixed-mix investment policy with a benefit policy that pays inflation-indexed benefits as long as ruin does not occur. This strategy is shown to be inefficient in many cases; the effective loss of capital can range from 5% to 15% under realistic parameter values. The inefficiency can be removed by adapting the investment policy and raising the benefits, without increasing the probability of ruin.

中文翻译：

---

机构支出效率和投资规则

摘要 捐赠基金和类似机构旨在在最初捐赠的资本的基础上产生无限期的收益流。为此，负责任的受托人需要设计支出政策和投资政策。如果根据该政策支付的福利的总净现值等于初始资本，则称支出和投资组合政策是有效的，如果总净现值小于该值，则称为无效。对于几种策略，在 Black-Scholes 假设下给出了总收益净现值的分析表达式。考虑的策略之一是将固定组合投资政策与福利政策相结合，只要不发生破产，就可以支付与通货膨胀挂钩的福利。这种策略在许多情况下被证明是低效的；在现实的参数值下，资本的有效损失可能在 5% 到 15% 之间。可以通过调整投资政策和提高收益来消除低效率，而不会增加破产的可能性。