Basic Stochastic Processes [Hardcover]

This book presents basic stochastic processes, stochastic calculus including Lévy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fair pricing play a central role and will be presented.

The authors also present basic concepts so that this series is relatively self-contained for the main audience formed by actuaries and particularly with ERM (enterprise risk management) certificates, insurance risk managers, students in Master in mathematics or economics and people involved in Solvency II for insurance companies and in Basel II and III for banks.

INTRODUCTION  xi

CHAPTER 1. BASIC PROBABILISTIC TOOLS FOR STOCHASTIC MODELING 1

1.1. Probability space and random variables 1

1.2. Expectation and independence 4

1.3. Main distribution probabilities 7

1.3.1. Binomial distribution 7

1.3.2. Negative exponential distribution 8

1.3.3. Normal (or Laplace–Gauss) distribution 8

1.3.4. Poisson distribution 11

1.3.5. Lognormal distribution 11

1.3.6. Gamma distribution 12

1.3.7. Pareto distribution 13

1.3.8. Uniform distribution 16

1.3.9. Gumbel distribution 16

1.3.10. Weibull distribution 16

1.3.11. Multi-dimensional normal distribution 17

1.3.12. Extreme value distribution 19

1.4. The normal power (NP) approximation 28

1.5. Conditioning 31

1.6. Stochastic processes 39

1.7. Martingales 43

CHAPTER 2. Hl“j