Continuous Time Martingales for Quantitative Finance

By Thomas Steiner — with the help of GNU R statistics / math software. see the source below, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=689096

A Martingale is simply a stochastic process (a sequence of random variables) for which, given some arbitrary time s < t, the conditional expectation of t given s is equal to the value at time s.

1. Definition

In the probability space:

Given a stochastic process X that is adapted to the filtration F(t) (i.e. is…