O'Reilly logo

Statistics for Finance by Erik Lindström, Henrik Madsen, Jan Nygaard Nielsen

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Appendix B

Probability theory

In this appendix it is the intention to give a brief overview of probability theory. Some of the concepts introduced are widely used in the lecture notes. It is not necessary to understand all the technical details, but an intuitive understanding of the concepts introduced is important.

B.1 Measures and σ-algebras

Let Ω denote a finite sample space which contains all the elementary outcome ωi for i = 1,2,..., N. In a two period binomial model the elementary outcome is the state of the world at time t = 2, which determines the stock price at that time.

Definition B.1 (σ-algebra).

Let Ω be a set of points ω. A family ℱ of subset of Ω is called a σ-algebra if

  • 1. Ø ∊
  • 2. A ∊ ℱ ⇒ Ac ∊ ℱ
  • 3. Anℱ for n=1,2,...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required