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18/05/2017

Probability


Pages: 160

Printbook: ISBN 9788885486096; $31.95

Pdf: ISBN 9788885486102; $16,99

Author: Erio Castagnoli, Margherita Cigola, Lorenzo Peccati

 

Table of 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

3.3 Conditional probability, correlation between events, stochastic independence and Bayes Theorem

 

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

5.4.1 The Poisson distribution

5.4.2 The binomial distribution

5.4.3 The exponential distribution

5.4.4 The normal distribution

5.4.5 The uniform distribution

 

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

6.5.1 The linear utility

6.5.2 The exponential utility

6.5.3 The logarithmic utility

6.5.4 The isoelastic utility

6.5.5 The quadratic utility

 

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

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