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2010
Book
Titel
Monte Carlo methods and models in finance and insurance
Abstract
This book is intended as an introduction to both Monte Carlo methods and financial and actuarial models. Although the technicalities are often avoided, the authors go for more than standard models and methods. The authors believe that the book can be used as an introductory text to finance and insurance for both numerical analysts as well as for the practitioners working in banks and insurance companies. Finally the book can be also used as a cooking book via the collection of the different algorithms that are explicitly stated where they are developed. \par The book starts with a survey on random number generation and basics of Monte Carlo methods. The application of these methods to stochastic processes of diffusion type is the next step. To that purpose, basics of diffusion processes and Itô calculus are provided with numerical methods for solving stochastic differential equations. The next chapter contains an introduction to both classical stock option pricing, more recent stock price models in different contexts, and interest rate models. A lot of applications of Monte Carlo in option pricing are given. In the next two chapters the interest is on stochastic processes that contain jumps as jump-diffusion or Lévy processes that can serve as building blocks for modeling the uncertainty inherent in financial markets. Finally, some applications of Monte Carlo for actuarial models are presented. The authors concentrate on premium principles, life and non-life insurance, and asset-liability management.