Basic Stochastic Processes (Mathematics and Statistics)
This book will present basic stochastic processes for building models in insurance, especially in life and non-life insurance as well as credit risk for insurance companies. Of course, stochastic methods are quite numerous; so we have deliberately chosen to consider to use those induced by two big families of stochastic processes: stochastic calculus including LÃ©vy processes and Markov and semi-Markov models. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values and fair pricing play a key role, and they will be presented in this volume.
This book is organized into seven chapters. Chapter 1 presents the essential probability tools for the understanding of stochastic models in insurance. The next three chapters are, respectively, devoted to renewal processes (Chapter 2), Markov chains (Chapter 3) and semi-Markov processes both homogeneous and non-time homogeneous (Chapter 4) in time. This fact is important as new nonhomogeneous time models are now becoming more and more used to build realistic models for insurance problems.
Chapter 5 gives the bases of stochastic calculus including stochastic differential equations, diffusion processes and changes of probability measures, therefore giving results that will be used in Chapter 6 devoted to LÃ©vy processes. Chapter 6 is devoted to LÃ©vy processes. This chapter also presents an alternative to basic stochastic models using Brownian motion as LÃ©vy processes keep the properties of independent and stationary increments but without the normality assumption.
Finally, Chapter 7 presents a summary of Solvency II rules, actuarial evaluation, using stochastic instantaneous interest rate models, and VaR methodology in risk management.
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|May 30, 2020|
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