Zeta Annuities, Fractional Calculus, and Polylogarithms
Zeta Annuities, Fractional Calculus, and Polylogarithms
Author(s): Jim TAOSubject(s): Economy, Business Economy / Management
Published by: ASERS Publishing
Keywords: variable annuities; interest theory; Riemann zeta function; fractional calculus; polylogarithms;
Summary/Abstract: We derive the present value and accumulated value formulas for zeta annuities-immediate, due, and continuously payable for all real values of s, thus generalizing annuity formulas like an and(Ia)n to the case where a payment of j−s is made at time j. Taking the limit n → ∞, the annuities become perpetuities, and the present value formula for a zeta perpetuity-immediate coincides with the polylogarithm.
Journal: Journal of Applied Economic Sciences (JAES)
- Issue Year: XVII/2022
- Issue No: 76
- Page Range: 162 - 172
- Page Count: 12
- Language: English
