*Article* **Accumulative Pension Schemes with Various Decrement Factors**

#### **Mohammed S. Al-Nator \*,† and Sofya V. Al-Nator †**

Department of Mathematics, Financial University under the Government of the Russian Federation, 49LeningradskyProspekt,Moscow125993,Russia; salnator@yandex.ru


Received: 18 October 2020; Accepted: 16 November 2020; Published: 22 November 2020

**Abstract:** We consider accumulative defined contribution pension schemes with a lump sum paymen<sup>t</sup> on retirement. These schemes differ in relation to inheritance and provide various decrement factors. For each scheme, we construct the balance equation and obtain an expression for calculation of gross premium. Payments are made at the end of the insurance event period (survival to retirement age or death or retirement for disability within the accumulation interval). A simulation model was developed to analyze the constructed schemes.

**Keywords:** pension schemes; balance equation; gross premium; premium load; lump sum; defined contribution pension schemes; decrement tables
