Applied Diffusion Processes from Engineering to Finance

The aim of this book is to promote interaction betweenengineering, finance and insurance, as these three domains havemany models and methods of solution in common for solving real-lifeproblems. The authors point out the strict inter-relations thatexist among the diffusion models used in engineering, finance andinsurance. In each of the three fields, the basic diffusion modelsare presented and their strong similarities are discussed.Analytical, numerical and Monte Carlo simulation methods areexplained with a view to applying them to obtain the solutions tothe different problems presented in the book. Advanced topics suchas nonlinear problems, Lévy processes and semi-Markov modelsin interactions with the diffusion models are discussed, as well aspossible future interactions among engineering, finance andinsurance. Contents 1. Diffusion Phenomena and Models. 2. Probabilistic Models of Diffusion Processes. 3. Solving Partial Differential Equations of Second Order. 4. Problems in Finance. 5. Basic PDE in Finance. 6. Exotic and American Options Pricing Theory. 7. Hitting Times for Diffusion Processes and Stochastic Models inInsurance. 8. Numerical Methods. 9. Advanced Topics in Engineering: Nonlinear Models. 10. Lévy Processes. 11. Advanced Topics in Insurance: Copula Models and VaRTechniques. 12. Advanced Topics in Finance: Semi-Markov Models. 13. Monte Carlo Semi-Markov Simulation Methods. About the Authors Jacques Janssen is now Honorary Professor at the Solvay BusinessSchool (ULB) in Brussels, Belgium, having previously taught atEURIA (Euro-Institut d'Actuariat, University of WestBrittany, Brest, France) and Télécom-Bretagne (Brest,France) as well as being a director of Jacan Insurance and FinanceServices, a consultancy and training company. Oronzio Manca is Professor of thermal sciences at SecondaUniversità degli Studi di Napoli in Italy. He is currentlyAssociate Editor of ASME Journal of Heat Transfer and Journal ofPorous Media and a member of the editorial advisory boards for TheOpen Thermodynamics Journal, Advances in Mechanical Engineering,The Open Fuels & Energy Science Journal. Raimondo Manca is Professor of mathematical methods applied toeconomics, finance and actuarial science at University of Rome"La Sapienza" in Italy. He is associate editor for thejournal Methodology and Computing in Applied Probability. His mainresearch interests are multidimensional linear algebra,computational probability, application of stochastic processes toeconomics, finance and insurance and simulation models.