Money and Mathematics

1. Front Matter

   Pages i-xiv

   PDF

2. Income Taxes, Lottery, and Lion Hunting—Elementary Mathematics

   1. Front Matter

      Pages 1-1

      PDF

   2. “We Take over Your VAT!” How Big Is the Actual Discount?

      • Ralf Korn, Bernd Luderer

      Pages 3-3

   3. Millions Every Week, but Not for Me. Six Numbers in the Lottery

      • Ralf Korn, Bernd Luderer

      Pages 5-7

   4. Where Did My Money Go? Loss Compensation After a Price Drop

      • Ralf Korn, Bernd Luderer

      Pages 9-11

   5. How Do You Catch a Lion? Finding a Zero by Halving the Interval

      • Ralf Korn, Bernd Luderer

      Pages 13-16

   6. Upside Down and Up Again. How Many Zeros Does a Polynomial Have?

      • Ralf Korn, Bernd Luderer

      Pages 17-20

   7. “According to Adam Ries, that Comes to …” About Fusti, Freight, and Cartage

      • Ralf Korn, Bernd Luderer

      Pages 21-24

   8. How to Invest? The Cost-Average Effect

      • Ralf Korn, Bernd Luderer

      Pages 25-27

   9. § 32a, the Politician and the Coaster. Calculating the Income Tax of a Person

      • Ralf Korn, Bernd Luderer

      Pages 29-31

   10. This Makes the Taxpayer Shudder. What Does “Cold Progression” Actually Mean?

       • Ralf Korn, Bernd Luderer

       Pages 33-37

3. Interest Rates, Prices, Yields—Classical Financial Mathematics

   1. Front Matter

      Pages 39-39

      PDF

   2. A Fair Deal? Or: There’s Nothing Like Starting Young

      • Ralf Korn, Bernd Luderer

      Pages 41-42

   3. Should I Pay the Bill Quickly? Cash Discount

      • Ralf Korn, Bernd Luderer

      Pages 43-44

   4. The Children of the Interest Rate Are the Grand-Children of the Capital. Compound Interest

      • Ralf Korn, Bernd Luderer

      Pages 45-48

   5. When Will Scrooge McDuck Be Satisfied? The Doubling Problem

      • Ralf Korn, Bernd Luderer

      Pages 49-52

   6. How Real Is Nominal? The Actual Rate of Return on a Principal

      • Ralf Korn, Bernd Luderer

      Pages 53-56

   7. “Have I Learned to Calculate Correctly?” Why Dr. X. from Gifhorn Was Wrong

      • Ralf Korn, Bernd Luderer

      Pages 57-58

   8. “What, I Have to Pay that Long?” Full Repayment of a Loan

      • Ralf Korn, Bernd Luderer

      Pages 59-61

   9. The Widow of the General and the Painter. A Loan à la Chekhov

      • Ralf Korn, Bernd Luderer

      Pages 63-66

This book follows a conversational approach in five dozen stories that provide an insight into the colorful world of financial mathematics and financial markets in a relaxed, accessible and entertaining form. The authors present various topics such as returns, real interest rates, present values, arbitrage, replication, options, swaps, the Black-Scholes formula and many more. The readers will learn how to discover, analyze, and deal with the many financial mathematical decisions the daily routine constantly demands.

The book covers a wide field in terms of scope and thematic diversity. Numerous stories are inspired by the fields of deterministic financial mathematics, option valuation, portfolio optimization and actuarial mathematics. The book also contains a collection of basic concepts and formulas of financial mathematics and of probability theory. Thus, also readers new to the subject will be provided with all the necessary information to verify the calculations.

 

• Mathematics made easy
• Financial strategies
• Understanding financial markets
• Risk and return
• Measurement of risk
• Interest rate mathematics
• Insurance mathematics
• Mathematical finance
• Quantitative finance

“The book is a part of Springer Texts … suited for both the class and self-study. … this book is a wonderful resource on the various aspects of money and mathematics. In a world that pervades with concepts related to insurance, annuities, discounts, bargains, options, and risks, this book could come as an eye-opener to many. The readers are going to find this book enriching and satiating. The book is worth every second spent reading it.” (Firdous Ahmad Mala, Journal of Economics, Vol. 137 (3), 2022)

• Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany

  Ralf Korn

• Fakultät für Mathematik, TU Chemnitz, Chemnitz, Germany

  Bernd Luderer

Prof. Dr. Ralf Korn teaches at the Department of Mathematics at the University of Kaiserslautern (Germany). He collaborates with the Fraunhofer ITWM on research projects for the finance and insurance industry. He was previously the Chairman of the German Society for Insurance and Financial Mathematics (2015-2019) and has authored several successful books on financial mathematics. He is also the co-Editor of the European Actuarial Journal (Springer), and Editor of 'Series in Quantitative Finance' (World Scientific).


Prof. Dr. Bernd Luderer taught at the Faculty of Mathematics at the Chemnitz University of
Technology (Germany). He is the Editor of the German-language series 'Studienbücher Wirtschaftsmathematik' (Springer), and author of numerous successful textbooks on business and financial mathematics.

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