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**