Probability
A Brief Introduction
Published on 1. September 2017
156 pages
978-88-85486-10-2 (ISBN)
Description
Today probability turns out to be one of the most pervasive mathematical topics. It actually affects a number of quite different fields, proving particularly relevant to courses ranging from Statistics to Economics, from Finance to Management Science. Recently it has even found significant applications in some sectors of Law. This book contains a short presentation of the most basic aspects of probability theory. As a result, it should come in handy and help students grasp the main concepts of the discipline as well as acquire a basic probabilistic vocabulary, thus capturing at least the flavor of possible relevant applications. The book includes a sketch of von Neumann-Morgenstern utility theory, which is useful per se as well as being an enlightening bridge between probability and decision theories. The book also provides a substantial set of exercises with solutions.
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09/2017
Bocconi University Press
€59.56
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Persons
Erio Castagnoli is Contract Professor Senior of Mathematics at Bocconi University, Milan. His research interests focus on Optimization, Decision Theory, and Mathematical Finance. Margherita Cigola is Associate Professor of Mathematics at Bocconi University, Milan. Her research topics mainly concern Optimization and Mathematical Modelling for Decisions and Management. Lorenzo Peccati is Senior Full Professor of Mathematics at Bocconi University, Milan. Until 2014 he was Editor of the European Journal of Operational Research.
Content
- PROBABILITY
- Contents
- 1 General questions
- 2 The various approaches to probability theory
- 2.1 Classical probability
- 2.2 Frequency-based (or empirical) approach
- 2.3 The subjective approach: its relevance to Economics and Management
- 3 The axiomatic approach, or the maths of probability
- 3.1 Sample space and events
- 3.2 The axioms
- 4 Random numbers
- 4.1 What a random number is
- 4.2 The probability distribution of a random number
- 4.3 Computer simulation of random numbers
- 5 Expected value of (a function of) a random number
- 5.1 Moments
- 5.2 Moment generating function
- 5.3 Conditional random numbers and conditional expectations
- 5.4 A brief summary of standard distributions
- 6 Expected utility and certainty equivalent
- 6.1 The problem
- 6.2 The answer to the problem
- 6.3 The estimation of u
- 6.4 The notion of risk-aversion
- 6.5 Some popular utility functions
- 7 Random vectors: first notions
- 7.1 Notion of random vector
- 7.2 The probability distribution of a random vector
- 7.3 The notion of stochastic independence between two random numbers
- 7.4 The expectation of a random vector
- 7.5 The expectation of a function of a random vector
- 7.6 Second order moments for random vectors
- 7.7 The variance of a linear function of random numbers
- 8 Exercises
- References
- Index
- Back cover
