Probability for finance

Probability for Finance Patrick Roger Strasbourg University, EM Strasbourg Business School May 2010 Download free eBooks at bookboon.com Probability for Finance © 2010 Patrick Roger & Ventus Publishing ApS ISBN 978-87-7681-589-9 Download free eBooks at bookboon.com Contents Probability for Finance Contents Introduction 1.1 1.1.1 1.1.2 1.1.3 1.2 1.2.1 1.2.2 1.2.3 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 Probability spaces and random variables Measurable spaces and probability measures algebra (or tribe) on a set Sub-tribes of A Probability measures Conditional probability and Bayes theorem Independant events and independant tribes Conditional probability measures Bayes theorem Random variables and probability distributions Random variables and generated tribes Independant random variables Probability distributions and cumulative distributions Discrete and continuous random variables Transformations of random variables 10 10 11 13 16 18 19 21 24 25 25 29 30 34 35 2.1 Moments of a random variable Mathematical expectation 37 37 www.sylvania.com We not reinvent the wheel we reinvent light Fascinating lighting offers an ininite 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 beneit from international career paths Implement sustainable ideas in close cooperation with other specialists and contribute to inluencing our future Come and join us in reinventing light every day Light is OSRAM Click on the ad to read more Download free eBooks at bookboon.com Contents Probability for Finance 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 2.4.1 2.4.2 2.5 2.5.1 2.5.2 Expectations of discrete and continous random variables Expectation: the general case Illustration: Jensen’s inequality and Saint-Peterburg paradox Variance and higher moments Second-order moments Skewness and kurtosis The vector space of random variables Almost surely equal random variables The space L1 ( , A, P) The space L2 ( , A, P) Covariance and correlation Equivalent probabilities and Radon-Nikodym derivatives Intuition Radon Nikodym derivatives Random vectors Deinitions Application to portfolio choice 39 40 43 46 46 48 50 51 53 54 59 63 63 67 69 69 71 3.1 3.1.1 3.1.2 3.1.3 Usual probability distributions in inancial models Discrete distributions Bernoulli distribution Binomial distribution Poisson distribution 73 73 73 76 78 360° thinking Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities Click on the ad to read more Download free eBooks at bookboon.com .. .Probability for Finance Patrick Roger Strasbourg University, EM Strasbourg Business School May 2010 Download free eBooks at bookboon.com Probability for Finance © 2010 Patrick... Contents Probability for Finance Contents Introduction 1.1 1.1.1 1.1.2 1.1.3 1.2 1.2.1 1.2.2 1.2.3 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 Probability spaces and random variables Measurable spaces and probability. .. Sub-tribes of A Probability measures Conditional probability and Bayes theorem Independant events and independant tribes Conditional probability measures Bayes theorem Random variables and probability