# Continuous Time Martingales for Quantitative Finance

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…