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Computing present values by the AGM: Insurance and the Arithmetic-Geometric-Mean Iteration

by Burkhard Disch
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Current price ₹2,253.00
Original price ₹2,637.00
Original price ₹2,637.00
Original price ₹2,637.00
(-15%)
₹2,253.00
Current price ₹2,253.00

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Book cover type: Paperback
  • ISBN13: 9783640644445
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 24
  • Original Price: USD 26.9
  • Language: English
  • Edition: N/A
  • Item Weight: 41 grams
  • BISAC Subject(s): Industries / General

Scientific Essay from the year 2002 in the subject Business economics - Banking, Stock Exchanges, Insurance, Accounting, language: English, abstract: Summary Subject of this paper is a method for computing present values with the Arithmetic-Geometric-Mean iteration (AGM). The classical integral-fomula for present values - as for-mulated by Reichel 1] - is solved explicitly by approximating the integral using exponential or trigonometric sums. Using the Elliptic-Integral Presentation (first kind), sequences are con-structed which converge with second order accuracy in the case of exponential, sinus and co-sine functions. Thus, the present value is defined as the limit of a rapidly converging sequence. Examples demonstrate the procedures. Zusammenfassung Die Berechnung von Barwerten mit dem AGM Inhalt der Ausarbeitung ist die Berechnung von Barwerten mit dem Arithmetisch-Geometrischen-Mittel. Die bekannte Integraldarstellung von Reichel 1] wird explizit gel st unter Zu-hilfenahme einer Approximation des Integranden mit einer speziellen Form von Exponentialsummen oder trigonometrischen Polynomen. Durch die Darstellung des Grenzwertes des AGM mit dem Elliptischen Integral erster Art werden Folgen konstruiert, die quadratisch ge-gen die Exponentialfunktion bzw. Sinus und Cosinus konvergieren. Dadurch wird der Barwert durch eine rasch konvergente Folge dargestellt. Beispiele demonstrieren die Vorgehensweise.

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