Jacques Janssen & Oronzio Manca 
Applied Diffusion Processes from Engineering to Finance 

The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist among the diffusion models used in engineering, finance and insurance. In each of the three fields, the basic diffusion models are presented and their strong similarities are discussed. Analytical, numerical and Monte Carlo simulation methods are explained with a view to applying them to obtain the solutions to the different problems presented in the book. Advanced topics such as nonlinear problems, Lévy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance.

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 in Insurance.
8. Numerical Methods.
9. Advanced Topics in Engineering: Nonlinear Models.
10. Lévy Processes.
11. Advanced Topics in Insurance: Copula Models and Va R Techniques.
12. Advanced Topics in Finance: Semi-Markov Models.
13. Monte Carlo Semi-Markov Simulation Methods.

Table of Content

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

About the author

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.