Chapter 20

# Basic Stochastic Calculus

## 20.1 CHAPTER SUMMARY

In this chapter, we will introduce basic stochastic calculus using a very intuitive set of arguments capped off by solving some problems. In other words, we will introduce stochastic calculus in the way introductory calculus is usually taught, rather than in the way real analysis is typically taught.

## 20.2 Basics of Stochastic Calculus

In Chapter 19, we defined a Wiener or diffusion process based on the behavior of a binomial tree model as modeled by a random walk. These processes are also often known as Brownian motions. We can use these Wiener processes to develop random stock models. The first random stock model was due to Bachelier in 1905. Nowadays, we call that process arithmetic ...