“ A really efficient totalitarian state would be one in which the all-powerful executive of political bosses and their army of managers control a population of slaves who do not have to be coerced, because they love their servitude. To make them love it is the task assigned, in present-day totalitarian states, to ministries of propaganda, newspaper editors and schoolteachers.... The greatest triumphs of propaganda have been accomplished, not by doing something, but by refraining from doing. Great is truth, but still greater, from a practical point of view, is silence about truth. ”
by Aldous Huxley

Basic Notions

Basic notions of financial mathematics that the students should learn in a first course:

  • Arbitrage theorem (also called the fundamental theorem of financial mathematics)
  • Interest (different ways to calculate interest rates; general term structure of interest rates)
  • Non-arbitrage principle, martingale (risk-neutral) measures
  • Financial engineering products: forwards, futures, options, swaps, … why are they created, what are their uses, and their basic properties
  • Stochastic calculus (stochastic differential equation, Ito integral, Ito lemma)
  • Black-Scholes and some other derivatives pricing models
  • Risk (why risk management is important; measures of risk; hedging)
  • Elements of portfolio management / asset allocation

Recommended texts for a first course on financial mathematics:

  • Buchanan – An undergraduate introduction to financial mathematics – 2006. (As the title indicates, this book is well suited for undergraduate students)
  • Capinski and Zastawniak – Mathematics for finance: an introduction to financial engineering – 2004
  • Chourdakis – Financial engineering: a brief introduction using the Matlab system – 2008 (Matlab is one of the best computer software for doing finance)
  • Elliott and Kopp – Mathematics of financial markets, 2nd ed. – 2005
  • Focardi and Fabozzi – The mathematics of financial modeling and investment management – 2004
  • Harrison and Waldron – Mathematical economics and finance – 1998 (A rather elementary book, which also explains basic mathematical concepts such as linear algebra and elementray probability theory).
  • Hull – Options, futures, and other derivatives, 5th ed. (A rather comprehensive introduction to derivatives, which is still accessible to undergraduate students)
  • Lin – Lecture notes in mathematical finance – 1996 (This text is very mathematically-oriented)
  • Neftci – Principles of financial engineering, 2nd ed. – 2008 (a very good book with many real-world examples)
  • Pliska – Introduction to mathematical finance: discrete time models – 2001
  • Ross – An introduction to mathematical finance – 1999
  • Wilmott et al. – The mathematics of financial derivatives: a student introduction – 1996.

For Vietnamese students: I’m currently writing a textbook in Vietnamese, which will be available soon.

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