Applied Diffusion Processes from Engineering to Finance (eBook)

Jacques Janssen is now Honorary Professor at the Solvay Business School (ULB) in Brussels, Belgium, having previously taught at EURIA (Euro-Institut d'Actuariat, University of West Brittany, Brest, France) and Télécom-Bretagne (Brest, France) as well as being a director of Jacan Insurance and Finance Services, a consultancy and training company. Oronzio Manca is Professor of thermal sciences at Seconda Università degli Studi di Napoli in Italy. He is currently Associate Editor of ASME Journal of Heat Transfer and Journal of Porous Media and a member of the editorial advisory boards for The Open Thermodynamics Journal, Advances in Mechanical Engineering, The Open Fuels & Energy Science Journal. Raimondo Manca is Professor of mathematical methods applied to economics, finance and actuarial science at University of Rome "La Sapienza" in Italy. He is associate editor for the journal Methodology and Computing in Applied Probability. His main research interests are multidimensional linear algebra, computational probability, application of stochastic processes to economics, finance and insurance and simulation models.

Chapter 1 Diffusion phenomena and models

1.1 The origin of Diffusion processes

1.2 Problems in engineering

1.3 Problems in Finance and Insurance

Chapter 2 Basic mathematical aspects of diffusion processes

2.1 Probabilistic model of diffusion processes

2.2Continuum models of diffusion processes

Chapter 3 pricing problems in finance and interaction with diffusion theory

Chapter 4 Technical methods for solving diffusion problems

4.1 Fourier technique

4.2 Laplace transform

4.3 Green function

4.4 Risk neutral measure

Chapter 5 Numerical methods

5.1 Discretization methods

5.2 Finite elements

5.3 Finite difference/volume methods

5.4 Methods for SDE

Chapter 6 Monte Carlo methods

6.1 Presentation of the methods

6.2 Case of deterministic models

6.3 Case of stochastic models

Chapter 7 Solution of Problems in Engineering

Chapter 8 Solution of Problems in Finance and in Insurance Chapter 9 Advanced topics in Engineering

9.1 Non linear models

Chapter 10 Advanced topics in Finance

10.1 Lévy models

10.2 Semi-Markov models

10.3 Copula methods

Chapter 11 Advanced topics in Insurance

11.1 Semi-Markov models

11.2 Copula methods

Chapter 12 Present and future Interactions among Engineering, Finance and Insurance OMRMJJ

Appendix 1 Stochastic processes

Appendix 2 Itô Calculus

Appendix 3 Partial Differential equations

Appendix 4 n-Dimensional Matrices

References

Index