A Generalization of Discounted Central Limit Theorem and its Berry-Esseen Analogue

Abstract

Discounted central limit theorem was proved for i.i.d. random variables by Gerber (Theorem 2.1). This work is intended to extend the work of Gerber to the case where {??} is a periodic sequence of independent variables and ?i are periodic scalars. A simulation study was performed in order to support the result. We also give an interpretation of our work in a financial context. Finally, an example with real data is presented.

Keywords

• Berry-Esseen Theorem; Discount factor; Present value