Introduction to Stochastic Calculus and Its Applications

Stochastic Calculus deals with the rate of change of functions with respect to the randomness. It has been applied in the field of financial mathematics. When we look at the graph of stock prices, there are many irregular price fluctuations. The main tool for modeling the small fluctuations is the Brownian motion. This paper will mainly introduce the concept of Brownian motion, the concept of random walks, and the main flavors of stochastic calculus, Itô calculus. I will also discuss various applications, especially in the finance area