Money and Mathematics

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 ofTechnology (Germany). He is the Editor of the German-language series 'Studienbücher Wirtschaftsmathematik' (Springer), and author of numerous successful textbooks on business and financial mathematics.

“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)

• Part I: Income Taxes, Lottery, and Lion Hunting—Elementary Mathematics.- 1. “We Take over Your VAT!” How Big Is the Actual Discount?.- 2. Millions Every Week, but Not for Me. Six Numbers in the Lottery.- 3. Where Did My Money Go? Loss Compensation After a Price Drop.- 4. How Do You Catch a Lion? Finding a Zero by Halving the Interval.- 5. Upside Down and Up Again. How Many Zeros Does a Polynomial Have?.- 6. “According to Adam Ries, that Comes to . . . ” About Fusti, Freight, and Cartage.- 7. How to Invest? The Cost-Average Effect.- 8. § 32a, the Politician and the Coaster. Calculating the Income Tax of a Person.- 9. This Makes the Taxpayer Shudder. What Does “Cold Progression” Actually Mean?.- Part II: Interest Rates, Prices, Yields—Classical Financial Mathematics.- 10. A Fair Deal? Or: There’s Nothing Like Starting Young.- 11. Should I Pay the Bill Quickly? Cash Discount.- 12. The Children of the Interest Rate Are the Grand-Children of the Capital. Compound Interest.- 13. When Will Scrooge McDuck Be Satisfied? The Doubling Problem.- 14. How Real Is Nominal? The Actual Rate of Return on a Principal.- 15. “Have I Learned to Calculate Correctly?” Why Dr. X. from Gifhorn Was Wrong.- 16. “What, I Have to Pay that Long?” Full Repayment of a Loan.- 17. The Widow of the General and the Painter. A Loan à la Chekhov.- 18. Why Does Nominal not Equal Effective? The Effective Interest Rate of an Immediate Loan.- 19. Sandwich with a Car Inside. Financing with Hooks and Eyes.- 20. The Assiduous Clerk. Capital Certificates and Federal Bonds.- 21. 7500 Euros Monthly: A Lifetime. Or Better Yet, Two Millions Right Away?.- 22. Financing a Car with Zero Percent: A Bargain?- 23. Interest Payments Anytime: Isn’t That Wonderful? Continuous Compounding of Interest.- 24. Bearer Bonds and Coupons. Bond Prices and Returns of Bonds.- 25. Oops! A Law Containing Formulas and Numerical Methods? The Calculation of the Effective Interest Rate According to the German Price Indication Ordinance.- Part III: Financial Products and Strategies—Modern Financial Mathematics.- 26. Fair Prices and Market Prices.- 27. The Short End and the Long End. Yield Curves, Spot Rates, and Forward Rates.- 28. Simple as Vanilla Ice Cream. On Standard Financial Products.- 29. Exchanges for Mutual Benefit. Swaps.- 30. The Telescope That Has Been Pushed Together. How to Calculate a Swap Rate?.- 31. Pull out Yourself of the Swamp by Your Own Hair. The Bootstrapping Method.- 32. No Risk, No Fun! Risk Indicators of Fixed-Income Securities.- 33. Sleep Well Despite Turbulent Markets? The Immunization Property of the Duration.- 34. Rising Like a Phoenix from the Ashes. New Shine for Your Depot?.- 35. The Crop of Standing Corn. Are Speculators Really Bad People?.- 36. Orange Juice and Pork Bellies. Forward Transactions.- 37. Empty Pockets and No Money. About Short Sales and No-Arbitrage Portfolios.- 38. Earning Money Without Capital and Risk. Arbitrage Transactions and Fair Prices.- 39. Fibonacci and His Rabbits. A Few Words About Technical Analysis.- Part IV: Only Rights, No Obligations—Options.- 40. A Trip Around the World: Different Types of Options.- 41. Two Triumvirates: From Arbitrage to Speculation.- 42. Nothing Is for Free: The Arbitrage Principle.- 43. How Much Do I Have to Pay for My Right? Option Pricing According to Black and Scholes.- 44. It Takes Two: Option Pricing in the Binomial Model.- 45. Safe Behind the Hedge: Hedging of Stock Positions.- 46. Wrong Calculation—Right Result: Can This Really Be? The Correct Derivation of the Risk Measure Delta.- 47. The Greeks and the Risk: About Risk Indicators for Stock Options.- 48. “In, At and Out of the Money”: The Language of the Actors at the Financial Markets.- 49. Volatility Determines the Option Price—Really?.- 50. Speculating with Options: Rich by Using Leverage?.- Part V: It Is All in the Mix—Portfolio Theory.- 51. A Portfolio of Shares.- 52. Risky Investments: Everything Under Control.- 53. Negative with a Positive Impact: Risk Reduction Using Correlation.- 54. Above Your Needs and Maybe Even More? The CPPI Strategy.- 55. High Risk Pays Off!? Sometimes: On Strategies in Stock Market Games.- Part VI: The Collective Against Risks—Insurance.- 56. A Duo Taming Uncertainty: The Law of Large Numbers and the Central Limit Theorem.- 57. Do You like Classics? A German Life Insurance Concept.- 58. More Opportunities: Dynamic Hybrid Products.- 59. A Million Dollar Roulette in the Financial and Insurance Market? The Monte Carlo Method.- 60. Insurance for Millions–Billions for the Insurer.- 61. CRK: One Number for Risk and Return. Classification of Pension Products.- 62. Living with the Mortality Table.- 63. What Relates Honoré de Balzac and 30 Young Geneva Girls with Life Annuities and Life Tables?.- 64. Sometimes It Clicks and Sometimes Not. A Riester Pension Product with Index Participation.- Part VII: Theoretical Foundations—Classical and Stochastic Financial Mathematics.- Classical Financial Mathematics.- 66. Stochastic Financial Mathematics.