48 CHAPTER 1. BACKGROUND IDEAS
is intrinsically unobtainable.” If the dollar amounts get very large (so that
rationality no longer holds!), or only a few traders are involved, or sharp
jumps in prices occur, or the trades come too rapidly for information to
spread effectively, we must proceed with caution. The observed financial
outcomes may deviate from predicted ideal behavior in accurate scientific or
economic work, or financial engineering.
We must then alter our assumptions, re-derive the quantitative relation-
ships, perhaps with more sophisticated mathematics or introducing more
quantities and begin the cycle of modeling again.
Sources
Some of the ideas about mathematical modeling are adapted from the article
by Valencia [51] and the bookWhen Genius Failedby Roger Lowenstein.
Problems to Work for Understanding
Outside Readings and Links:
- Duke University Modeling Contest Team Accessed August 29, 2009
1.6 Randomness
Rating
Student: contains scenes of mild algebra or calculus that may require guid-
ance.
Section Starter Question
When we say something is “random”, what do we mean? What is the dic-
tionary definition of “random”?
Key Concepts
- Assigning probability 1/2 to the event that a coin will land heads and
probability 1/2 to the event that a coin will land tails is a mathematical