In actuarial science related to pension systems, it is widely assumed that the rate at which the reserves cover the payment of annuities (calculated for a given number of lives) is equal to the expected rate of return of the portfolios in which such reserves are invested. Given this assumption, pension fund managers may take greater risks to realize higher returns and subsequently reduce their pension liabilities. This study demonstrates that the discount rate used to calculate a two-life annuity and the expected return on the portfolio are not necessarily equal. A stochastic-based model is used to determine the proper discount rate for calculating the two-life annuity. The model includes fluctuations of both the interest rate and the payments made by the annuity. In general, this study contributes to the stability of pension systems by determining the appropriate discount rate when computing required actuarial reserves or the portfolio’s required rate of return given a reserve.

中文翻译：

---

精算模型，用于估算共同幸存者年金投资组合的最优回报率

在与养老金系统有关的精算科学中，广泛假设储备金支付年金支付的比率（针对给定生命数计算）等于投资于此类储备金的投资组合的预期回报率。在这种假设下，养老基金管理人可能会冒更大的风险来实现更高的回报并随后减少其养老金负债。这项研究表明，用于计算两用年金的折现率与投资组合的预期收益不一定相等。基于随机的模型用于确定适当的折现率，以计算两次生命年金。该模型包括利率和年金支付的波动。一般来说，