Lifeinsurance-tomfischer

Lifeinsurance-tomfischer - 1 Draft: Life insurance...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Draft: Life insurance mathematics in discrete time Tom Fischer Darmstadt University of Technology, Germany Lecture at the METU Ankara, Turkey April 12-16, 2004 2 A recent version of the lecture notes can be downloaded under www.mathematik.tu-darmstadt.de/ ˜ tfischer/Ankara.pdf This version is from April 27, 2004. Dr. Tom Fischer Technische Universit¨ at Darmstadt Fachbereich Mathematik, AG 9 Schloßgartenstr. 7 64289 Darmstadt Germany tfischer@mathematik.tu-darmstadt.de www.mathematik.tu-darmstadt.de/ ˜ tfischer 3 About these notes This is the preliminary (slide-form) version of the notes of a lecture at the Middle East Technical University in Ankara, Turkey, held by the author from April 12 to 16, 2004. As the audience was quite inhomogeneous, the notes contain a brief review of discrete time financial mathematics. Some notions and results from stochastics are explained in the Appendix. The notes contain several internet links to numerical spreadsheet examples which were developed by the author. The author does not (and cannot) guarantee for the correctness of the data supplied and the computations taking place. Tom Fischer CONTENTS 4 Contents 1 Introduction 9 1.1 Life insurance mathematics? . . . . . . . . . . . . . . . 10 1.2 Preliminary remarks . . . . . . . . . . . . . . . . . . . . 13 1.2.1 Intention . . . . . . . . . . . . . . . . . . . . . . 13 1.2.2 Warning . . . . . . . . . . . . . . . . . . . . . . 14 1.2.3 Benefits . . . . . . . . . . . . . . . . . . . . . . 15 1.3 Introductory examples . . . . . . . . . . . . . . . . . . . 16 1.3.1 Valuation in classical life insurance . . . . . . . . 16 1.3.2 Valuation in modern life insurance . . . . . . . . 18 2 A review of classical life insurance mathematics 19 2.1 Non-stochastic finance . . . . . . . . . . . . . . . . . . 20 CONTENTS 5 2.1.1 The model . . . . . . . . . . . . . . . . . . . . . 20 2.1.2 The present value of a cash flow . . . . . . . . . 21 2.2 Classical valuation . . . . . . . . . . . . . . . . . . . . . 23 2.2.1 The model . . . . . . . . . . . . . . . . . . . . . 23 2.2.2 The Expectation Principle . . . . . . . . . . . . . 25 2.3 The fair premium . . . . . . . . . . . . . . . . . . . . . 30 2.3.1 Life insurance contracts . . . . . . . . . . . . . . 30 2.3.2 The Principle of Equivalence . . . . . . . . . . . 31 2.4 Mortalities - The notation . . . . . . . . . . . . . . . . . 33 2.5 The reserve . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5.1 Definition and meaning . . . . . . . . . . . . . . 35 2.5.2 A recursive formula . . . . . . . . . . . . . . . . 36 2.6 Some contract forms . . . . . . . . . . . . . . . . . . . 38 CONTENTS 6 2.7 Spreadsheet examples . . . . . . . . . . . . . . . . . . . 39 2.8 Historical remarks . . . . . . . . . . . . . . . . . . . . . 40 3 Basic concepts of discrete time financial mathematics 44 3.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Portfolios and strategies . . . . . . . . . . . . . . . . . . 46 3.3 No-arbitrage and the Fundamental Theorem . . . . . . . 47No-arbitrage and the Fundamental Theorem ....
View Full Document

Page1 / 125

Lifeinsurance-tomfischer - 1 Draft: Life insurance...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online