Author of this section: Dr. Christof Luchsinger

If you are a mathematician, we suggest that you first read a simple, more economic introduction into this subject. If you do so, you will later on understand the motivations for many assumptions much better.

In this sense, we suggest you begin with Uszczapowski (in german, sorry to all our english visitors). The drawback of Uszczapowski is, as with all mathematical books written for a wider readership, that the more you advance, the more you find contradictions or unprecise information. Therefore we suggest you only read may be the first 150 to 200 pages and then choose a selection of the rest. Uszczapowski gives a detailed introduction into all sorts of financial products; this is not important to finance mathematicians.

• Optionen und Futures verstehen. I. Uszczapowski. Deutscher Taschenbuch Verlag, 1995

Mathematically more damanding, but still acceptable for economists is Hull. We strongy encourage Mathematicians working in the industry to read this book too.

• Options, Futures, and other Derivative Securities. J.C. Hull. Prentice Hall, 1999

Mathematically even more demanding are the script by Gmür and Baxter/Rennie. Economists with a strong background in Mathematics should be able to follow these books. Many proofs are omitted.

• Financial Calculus. M.W. Baxter & A.J.O. Rennie. Cambridge University Press, 1997 (More information about this book.)
• Kapitalmarktmodelle, Notizen zur Vorlesung, Wintersemester 1997/98. Dr. B. Gmür.Institut für Empirische Wirtschaftsforschung der Universität Zürich, 1997 (bruno.gmuer@juliusbaer.com)

Among those books with rigorous mathematics (omitting only few proofs) we suggest the following for discrete time

• Introduction to Mathematical Finance, discrete time models. S.R. Pliska. Blackwell Publishers, 1997
• Mathematical Finance and Probability, A discrete Introduction. P. Koch Medina & S. Merino, Birkhäuser, 2003

and for both, discrete and continuous time, we suggest

• Einführung in die Finanzmathematik, Vorlesungsskript 2000, Dr. Christof Luchsinger (jobs@math-jobs.com)
• Introduction to Stochastic Calculus Applied to Finance. D. Lamberton & B. Lapeyre (LL). Chapman & Hall, 1996
• Martingale Methods in Financial Modelling. M. Musiela & M. Rutkowski (MR). Springer, 2004
• Risk-Neutral Valuation by N.H. Bingham and R. Kiesel (BK), Springer 2003
• Methods of Mathematical Finance. I. Karatzas and S.E. Shreve (KS2). Springer 1998 ISBN 0-387-94839-2
• Options Markets. J.C. Cox & M. Rubinstein (CR). Prentice Hall, 1985

A broad treatment of mathematical Finance can be found in Karatzas/Shreve.

• Methods of Mathematical Finance. I. Karatzas and S.E. Shreve. Springer 1998 ISBN 0-387-94839-2

A detailed, vivid treatment of stochastic integration can be found in Øksendal (stochastic integration with respect to the Brownian Motion only). Mathematically very demanding is "Brownian Motion and Stochastic Calculus".

• Stochastic Differential Equations; An Introduction with Applications. B. Øksendal (Ø), Springer, 2003.
• Brownian Motion and Stochastic Calculus by I. Karatzas and S.E. Shreve (KS1). Springer 1997

More "Suggested Readings" can be found in Pliska on pages vii - ix.

Webmaster: Dr. Christof Luchsinger / jobs@math-jobs.com / Member of the Luchsinger Mathematics Group