Probability for finance

2 Probability for Finance Patrick Roger Strasbourg University, EM Strasbourg Business School May 2010 Download free eBooks at bookboon.com... Probability for Finance4 Contents Contents

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

Probability for Finance

4

Contents

Contents

1.1 Measurable spaces and probability measures 10

1.1.1 algebra (or tribe) on a set 11

1.2 Conditional probability and Bayes theorem 18

1.2.1 Independant events and independant tribes 19

1.2.2 Conditional probability measures 21

1.3 Random variables and probability distributions 25

1.3.1 Random variables and generated tribes 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

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Probability for Finance

5

Contents

2.1.1 Expectations of discrete and continous random variables 39

2.1.2 Expectation: the general case 40

2.1.3 Illustration: Jensen’s inequality and Saint-Peterburg paradox 43

2.2 Variance and higher moments 46

2.3 The vector space of random variables 50

2.3.1 Almost surely equal random variables 51

2.3.2 The space L1 ( , A, P) 53

2.3.4 Covariance and correlation 59

2.4 Equivalent probabilities and Radon-Nikodym derivatives 63

2.4.2 Radon Nikodym derivatives 67

2.5.2 Application to portfolio choice 71

3 Usual probability distributions in inancial models 73

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