Basic Stochastic Processes
Publication Date: August 2015 Hardback 326 pp.
In this book, the authors focus on two big families of stochastic processes: stochastic calculus, including Lévy processes, and Markov and semi-Markov models. From a financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values and fair pricing play a central role and will be presented.
The first chapter presents the essential probability tools for understanding stochastic models in insuranceand the next three chapters are respectively devoted to renewal processes, Markov chains and semi-Markov processes in both homogeneous and non-homogeneous time.
Chapter 5 gives the bases of stochastic calculus, whilst Chapter 6 is devoted to Lévy processes.
Finally, Chapter 7 presents a summary of Solvency II rules, actuarial evaluation, using stochastic instantaneous interest rate models and VaR methodology in risk management.
The authors also present basic concepts so that the book is relatively self-contained, at least for the main audience formed of actuaries (particularly those with the ERM certificate), insurance risk managers, Masters students in mathematics or economics and those involved in Solvency II for insurance companies and in Basel II and III for banking.
1. Basic Probabilistic Tools for Stochastic Modeling.
2. Homogeneous and Non-homogeneous Renewal Models.
3. Markov Chains.
4. Homogeneous and Non-homogeneous Semi-Markov Models.
5. Stochastic Calculus.
6. Lévy Processes.
7. Actuarial Evaluation, VaR and Stochastic Interest Rate Models.
About the Authors
Pierre Devolder is Professor of quantitative finance and actuarial sciences.
Jacques Janssen is Honorary Professor at the Solvay Business School in Brussels, Belgium and a member of Belgian, Swiss and French actuarial associations. His main research interests include stochastic processes, financial and actuarial mathematics, operations research and data mining.
Raimondo Manca is Professor of mathematical methods applied to economics, finance and actuarial science.