Modern legislation has increased the amount of quantities that insurance companies should report in order to prove solvent as well as prudent. More of these quantities require not just simple bookkeeping but a mere projection of the future. In this paper, we provide a solid base for this crystal ball exercise as we derive differential equations for the retrospective reserves of a pension company, in a setting where the surplus and the dividends are modelled. The differential equations rely on dynamics of the stochastic reserve that are affine functions of the stochastic reserve themselves. The retrospective reserves are defined as conditional expected values, given limited information, leading to computational tractable differential equations for the reserves. We wrap up the theoretical part by suggestions for practical use in terms of considering validation of guarantees and discretionary benefits at future time points.

现代立法增加了保险公司应报告的数量，以证明有偿付能力和审慎性。更多的这些数量不仅需要简单的簿记，还需要对未来的预测。在本文中，我们为这种水晶球练习提供了坚实的基础，因为我们在对盈余和股息进行建模的情况下推导出了养老金公司的追溯储备的微分方程。微分方程依赖于作为随机储备本身的仿射函数的随机储备的动力学。追溯储量被定义为条件预期值，在有限信息的情况下，导致储量的计算微分方程。