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Polynomial Expansion of the Future Value Factor for an Annuity Due : Generalization via the Hockey-stick Identity and Binomial Theorem
http://hdl.handle.net/10232/0002002252
http://hdl.handle.net/10232/00020022521c86e83e-c3bb-412f-87b3-704162f467b4
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
03890104_106_p50-58.pdf (1.4 MB)
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| アイテムタイプ | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2026-04-16 | |||||
| タイトル | ||||||
| タイトル | Polynomial Expansion of the Future Value Factor for an Annuity Due : Generalization via the Hockey-stick Identity and Binomial Theorem | |||||
| タイトル言語 | en | |||||
| 著者 |
Shiraishi, Shunsuke
× Shiraishi, Shunsuke× Wu, Boyu× Wang, Jingkai |
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| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | departmental bulletin paper | |||||
| アクセス権 | ||||||
| アクセス権 | open access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||
| 要約 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | This paper derives an m-th order approximation formula, denoted by Sm(r) for the future value annuity factor (FVAF) of an annuity due and analyzes its mathematical properties. While the FVAF is typically defined as the sum of a geometric series, polynomial approximation is highly effective in practical simulations when the interest rate is small. This paper presents two distinct mathematical approaches to derive a general approximation formula Sm(r) for the FVAF. The first approach applies the binomial theorem to the expanded form (A) of the FVAF and consolidates the resulting coefficients using the hockey-stick identity. The second approach starts from the closed-form expression (B) of the FVAF and achieves the same result as the first approach by integrating terms through algebraic operations and Pascal’s rule. By demonstrating that these two methods converge to the same general approximation formula, this paper provides a robust mathematical foundation for the validity of the general approximation formula for the FVAF. The results of this research contribute to an intuitive understanding of the close relationship between combinatorics and financial mathematics. |
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| 内容記述言語 | en | |||||
| 収録雑誌名 |
ja : 経済学論集 en : Journal of economics and sociology, Kagoshima University 巻 106, p. 50-58, 発行日 2026-04-10 |
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| 作成日 | ||||||
| 日付 | 2026-04-10 | |||||
| 日付タイプ | Issued | |||||
| ISSN | ||||||
| 収録物識別子タイプ | PISSN | |||||
| ISSN | 03890104 | |||||
| NII書誌ID（雑誌） | ||||||
| 収録物識別子タイプ | NCID | |||||
| NC ID | AN00070433 | |||||
| 出版タイプ | ||||||
| 出版タイプ | VoR | |||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
| 公開者・出版者 | ||||||
| 出版者 | 鹿児島大学 | |||||
| 出版者言語 | ja | |||||
| 公開者・出版者 | ||||||
| 出版者 | Kagoshima University | |||||
| 出版者言語 | en | |||||
