Chapter 6

Question 1

Define brownian motion

Answer 1

A Brownian motion with variance parameter σ2 is a continuous
time process {Wt , t ≥ 0} with state space X = R such that
1. W0 = 0,
2. {Wt } has independent increment
3. for any s < t, Wt − Ws ∼ N (0, σ2(t − s))

Question 2

Define standard brownian motion

Answer 2

Brownian motion such that variance parameter is 1

Question 3

What are two traits for the function t going to Wt

Answer 3

It is continuous with probability 1 but it is nowhere differentiable with probability 1 - because its very erratic

Question 4

What is the idea of the reflection principle

Answer 4

what is the probability distribution of the maximum of
the Brownian motion on a given interval?

Question 5

What is reimann integral

Answer 5

Simple way to approximate the area under a curve from a to b

Question 6

What is Xi and Wi representing in betting strategy

Answer 6

The amount of shares I buy - Xi
Wi - price of a given share

Question 7

What does a process being non anticipating mean

Answer 7

It is a function of past values only

Question 8

Why is brownian motion usually a poor model for share price

Answer 8

It can take negative values - better model would be exp(gamma Wt)

Question 9

What is df(t) the same as?

Answer 9

intergration