O'Reilly logo

Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach by Hong Xie, Chaoqun Ma, Guojun Gan

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

CHAPTER 13

EXPECTATION

In probability theory, the expectation of a random variable is the integral of the random variable with respect to its probability measure. For example, the expectation of a discrete random variable is the weighted average of all possible values that the random variable can take on. In this chapter, we shall introduce the definition of expectation and relevant concepts.

13.1 Basic Concepts and Facts

Definition 13.1 (Expectation). Let (Ω, , P) be a probability space and X L1 (Ω, , P), where L1(Ω, , P) denotes the set of all P-integrable functions on Ω, (see Definition 6.4). The expectation E(X) of X is defined as

equation

Definition 13.2 (Expectation over Subsets). Let (Ω, , P) be a probability space, F , and X be a random variable on Ω. Then E(X; F) is defined as

where

Definition ...

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