Fractional Age Assumption Based on Cubic Polynomial Interpolation

Abstract

This article proposes a new fractional age assumption (FAA) based on the cubic polynomial interpolation (CPI) and applies it to estimate the mortality rate and related actuarial quantities. The validity of the method under CPI is proved theoretically and the valuable advantages of CPI assumption are discussed based on three different perspectives—utilized death information, property of mortality force, and optimality criterion. The results show that CPI assumption has distinct valuable superiority compared with other FAAs in references. Finally under CPI assumption we study the calculations of some important actuarial quantities in life contingencies.

Keywords:

• Actuarial present value
• Cubic polynomial interpolation
• Force of mortality
• Fractional age assumption
• Survival function

• Mathematics Subject Classification
• Primary 62P05
• Secondary 65D05

Funding

This work was partially supported by NSFC (No. 71071088) and Shandong Foundation of Natural Science (No. ZR2010GL014).