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Summary

The aim of this book is to promote interaction between Engineering, Finance and Insurance, as there are many models and solution methods in common for solving real-life problems in these three topics.
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 get the solutions of the different problems presented in the book. Advanced topics such as non-linear 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.

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

Supplemental Materials

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