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. […]
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.