Search for tag: "stochastic processes"

Let's look at Pairs Trading as a way to get started (Google Drive)

Let's understand the multidimensional Ito formula (Google Drive)

Let's prove the standard Ito formula (in one dimension) (Google Drive)

Let's rigorously prove Ito's formula for the square of Brownian motion (Google Drive)

Let's review the proof of the standard chain rule as an introduction to several tools we will use to understand Ito's formula (Google Drive)

Let's work through several examples of Ito integrals (Google Drive)

We understand some properties of Ito integrals (Google Drive)

We define Ito Integrals (Google Drive)

We cover martingales, which are the background for Ito integration (Google Drive)

Let's look at the Quadratic Variation of Brownian motion, and motivate a simple example of Ito's rule (Google Drive)

Let's look at returns and log returns (Google Drive)

Let's understand sigma algebras and how they interact with conditional expectation (Google Drive)

Let's understand some properties of conditional expectation (Google Drive)

Let's define conditional expectation and probability (Google Drive)

Let's look at th evolution of information in Brownian motion (Google Drive)

Let's do some calculations with Brownian motion (Google Drive)

Let's characterize Brownian motion (Google Drive)

Let's construct Brownian motion from a random walk (Google Drive)

Gaussian moments (Google Drive)

Review of tails of Gaussians; (Google Drive)

Review of Gaussian densities (Google Drive)