Applied Diffusion Processes from Engineering to Finance [Hardcover]

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, L?vy processes and semi-Markov models in interactions with the diffusion models are discussed, as well as possible future interactions among engineering, finance and insurance.

Introduction xiii

Chapter 1 Diffusion Phenomena and Models 1

1.1 General presentation of diffusion process 1

1.2 General balance equations 6

1.3 Heat conduction equation 10

1.4 Initial and boundary conditions 12

Chapter 2 Probabilistic Models of Diffusion Processes 17

2.1 Stochastic differentiation 17

2.2 It?s formula 19

2.3 Stochastic differential equations (SDE) 24

2.4 It? and diffusion processes 28

2.5 Some particular cases of diffusion processes 32

2.6 Multidimensional diffusion processes 36

2.7 The StroockVaradhan martingale characterization of diffusions (Karlin and Taylor) 41

2.8 The FeynmanKac formula (Platen and Heath) 42

Chapter 3 Solving Partial Differential Equations of Second Order 47

3.1 Basic definitions on PDE of second order 47