Ito Calculus
Overview
Ito Lemma
{% dt^2 = 0 %}
{% dt \times dW = 0 %}
{% dW^2 = dt %}
Multidimensional Ito Lemma
{% Z=XY %}
{% \frac{dZ}{Z} = \frac{dX}{X} + \frac{dY}{Y} +\frac{dX}{X} \frac{dY}{Y} %}
(see Back pg 37)
{% Z=\frac{Y}{X} %}
{% \frac{dZ}{Z} = \frac{dY}{Y} - \frac{dX}{X} - \frac{dX}{X} \frac{dY}{Y} + \frac{dX}{X} ^2 %}
{% Z= e^X %}
{% \frac{dZ}{Z} = dX + \frac{dX ^ 2}{2} %}
{% Z= log(X) %}
{% dZ = \frac{dX}{X} - \frac{1}{2} (\frac{dX}{X})^2 %}
