probability for finance

Patrick Roger
Probability for Finance
Download free books at
Download free eBooks at bookboon.com
2
Probability for Finance
Patrick Roger
Strasbourg University, EM Strasbourg Business School
May 2010
Download free eBooks at bookboon.com
3
Probability for Finance
© 2010 Patrick Roger & Ventus Publishing ApS
ISBN 978-87-7681-589-9
Download free eBooks at bookboon.com
Click on the ad to read more
Probability for Finance
4
Contents
Contents
Introduction 8
1. Probability spaces and random variables 10
1.1 Measurable spaces and probability measures 10
  
1.1.2 Sub-tribes of A 13
1.1.3 Probability measures 16
1.2 Conditional probability and Bayes theorem 18
1.2.1 Independant events and independant tribes 19
1.2.2 Conditional probability measures 21
1.2.3 Bayes theorem 24
1.3 Random variables and probability distributions 25

  
1.3.2 Independant random variables 29
1.3.3 Probability distributions and cumulative distributions 30
1.3.4 Discrete and continuous random variables 34
1.3.5 Transformations of random variables 35
2. Moments of a random variable 37
2.1 Mathematical expectation 37


www.sylvania.com
We do not reinvent
the wheel we reinvent
light.
Fascinating lighting offers an infinite spectrum of
possibilities: Innovative technologies and new
markets provide both opportunities and challenges.
An environment in which your expertise is in high
demand. Enjoy the supportive working atmosphere
within our global group and benefit from international
career paths. Implement sustainable ideas in close
cooperation with other specialists and contribute to
influencing our future. Come and join us in reinventing
light every day.
Light is OSRAM
Download free eBooks at bookboon.com
Click on the ad to read more
Probability for Finance
5
Contents
2.1.1 Expectations of discrete and continous random variables 39

  
  
  
2.2.1 Second-order moments 46
2.2.2 Skewness and kurtosis 48
2.3 The vector space of random variables 50
2.3.1 Almost surely equal random variables 51
2.3.2 The space L
1
 
2.3.3 The space L
2

 
2.3.4 Covariance and correlation 59
2.4 Equivalent probabilities and Radon-Nikodym derivatives 63
2.4.1 Intuition 63
2.4.2 Radon Nikodym derivatives 67
2.5 Random vectors 69
  
2.5.2 Application to portfolio choice 71
  
3.1 Discrete distributions 73
3.1.1 Bernoulli distribution 73
3.1.2 Binomial distribution 76
3.1.3 Poisson distribution 78

360°
thinking
.

© Deloitte & Touche LLP and affiliated entities.
Discover the truth at www.deloitte.ca/careers