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 . Patrick Roger Probability for Finance Download free books at Download free eBooks at bookboon.com 2 Probability for Finance Patrick Roger Strasbourg University,. 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. 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