ABSTRACT
Consider a particle moving around the integers. At time 0, the particle is at the origin and moves one step right or left with some probability. Such a mathematical model is called a random walk and used to describe random phenomena in diverse areas of physics, economics, and finance. In particular, random walks are the basis of the binomial model for the securities market, the main theme of the next chapter. This chapter provides a concise summary of the theory of random walks useful in finance. Note, however, that the theory of random walks is very rich, and the results provided here are indeed only ‘the tip of the iceberg’. See, e.g., Feller (1957) for details.
