Computing present values by the AGM

Insurance and the Arithmetic-Geometric-Mean Iteration

Business & Finance, Finance & Investing, Banks & Banking
Cover of the book Computing present values by the AGM by Burkhard Disch, GRIN Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Burkhard Disch ISBN: 9783640643561
Publisher: GRIN Publishing Publication: June 16, 2010
Imprint: GRIN Publishing Language: English
Author: Burkhard Disch
ISBN: 9783640643561
Publisher: GRIN Publishing
Publication: June 16, 2010
Imprint: GRIN Publishing
Language: English

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 gelöst 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 gelöst 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.

More books from GRIN Publishing

Cover of the book Impact of restructuring and privatization on the performance of the electricity sector in Nigeria by Burkhard Disch
Cover of the book The Baltic Sea Region by Burkhard Disch
Cover of the book MBA-Programmes and MBA-Students of Kannur University (India) and Riedlingen University (Germany) by Burkhard Disch
Cover of the book The Double motif in literature using the example of Stevenson's 'The Strange Case of Dr. Jekyll and Mr. Hyde' by Burkhard Disch
Cover of the book A Never-Ending Quarrel - Bob Dylan and Society by Burkhard Disch
Cover of the book Communism - Two different views by Burkhard Disch
Cover of the book Jewishly Universal - Woody Allen's Film-Persona, its Jewish Roots and Universal Appeal, with references to Annie Hall and Manhattan by Burkhard Disch
Cover of the book Solidarity in Athol Fugards Township Plays by Burkhard Disch
Cover of the book The use of Facebook by companies by Burkhard Disch
Cover of the book Repräsentativitätsheurisik - Eine Einführung by Burkhard Disch
Cover of the book The Concept of Metamorphosis in Literature by Burkhard Disch
Cover of the book Constructing the Social Problem: Causes of Drug Addiction in Early Soviet Medical Texts by Burkhard Disch
Cover of the book South African foreign policy and SADC goals - lockstep or deadlock? by Burkhard Disch
Cover of the book People on the net. Can the internet can our culture and world view? by Burkhard Disch
Cover of the book Dr. Robert Waller: Visionary Leader and Skilled Manager by Burkhard Disch
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy