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作者 Janssen, Jacques
書名 Applied Diffusion Processes from Engineering to Finance
出版項 Hoboken : John Wiley & Sons, Incorporated, 2013
©2013
國際標準書號 9781118578346 (electronic bk.)
9781118578339
book jacket
版本 1st ed
說明 1 online resource (315 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Iste
Iste
附註 Intro -- Contents -- Title Page -- Copyright Page -- Introduction -- Chapter 1: Diffusion Phenomena and Models -- 1.1. General presentation of diffusion process -- 1.2. General balance equations -- 1.3. Heat conduction equation -- 1.4. Initial and boundary conditions -- Chapter 2: Probabilistic Models of Diffusion Processes -- 2.1. Stochastic differentiation -- 2.2. Itô's formula -- 2.3. Stochastic differential equations (SDE) -- 2.4. Itô and diffusion processes -- 2.5. Some particular cases of diffusion processes -- 2.6. Multidimensional diffusion processes -- 2.7. The Stroock-Varadhan martingale characterization of diffusions (Karlin and Taylor [KAR 81]) -- 2.8. The Feynman-Kac formula (Platen and Heath [PLA 06]) -- Chapter 3: Solving Partial Differential Equations of Second Order -- 3.1. Basic definitions on PDE of second order -- 3.2. Solving the heat equation -- 3.3. Solution by the method of Laplace transform -- 3.4. Green's functions -- Chapter 4: Problems in Finance -- 4.1. Basic stochastic models for stock prices -- 4.2. The bond investments -- 4.3. Dynamic deterministic continuous time model for instantaneous interest rate -- 4.4. Stochastic continuous time dynamic model for instantaneous interest rate -- 4.5. Multidimensional Black and Scholes model -- Chapter 5: Basic PDE in Finance -- 5.1. Introduction to option theory -- 5.2. Pricing the plain vanilla call with the Black-Scholes-Samuelson model -- 5.3. Pricing no plain vanilla calls with the Black-Scholes-Samuelson model -- 5.4. Zero-coupon pricing under the assumption of no arbitrage -- Chapter 6: Exotic and American Options Pricing Theory -- 6.1. Introduction -- 6.2. The Garman-Kohlhagen formula -- 6.3. Binary or digital options -- 6.4. "Asset or nothing" options -- 6.5. Numerical examples -- 6.6. Path-dependent options -- 6.7. Multi-asset options -- 6.8. American options
Chapter 7: Hitting Times for Diffusion Processes and Stochastic Models in Insurance -- 7.1. Hitting or first passage times for some diffusion processes -- 7.2. Merton's model for default risk -- 7.3. Risk diffusion models for insurance -- Chapter 8: Numerical Methods -- 8.1. Introduction -- 8.2. Discretization and numerical differentiation -- 8.3. Finite difference methods -- Chapter 9: Advanced Topics in Engineering: Nonlinear Models -- 9.1. Nonlinear model in heat conduction -- 9.2. Integral method applied to diffusive problems -- 9.3. Integral method applied to nonlinear problems -- 9.4. Use of transformations in nonlinear problems -- Chapter 10: Lévy Processes -- 10.1. Motivation -- 10.2. Notion of characteristic functions -- 10.3. Lévy processes -- 10.4. Lévy-Khintchine formula -- 10.5. Examples of Lévy processes -- 10.6. Variance gamma (VG) process -- 10.7. The Brownian-Poisson model with jumps -- 10.8. Risk neutral measures for Lévy models in finance -- 10.9. Conclusion -- Chapter 11: Advanced Topics in Insurance: Copula Models and VaR Techniques -- 11.1. Introduction -- 11.2. Sklar theorem (1959) -- 11.3. Particular cases and Fréchet bounds -- 11.4. Dependence -- 11.5. Applications in finance: pricing of the bivariate digital put option [CHE 04] -- 11.6. VaR application in insurance -- Chapter 12: Advanced Topics in Finance: Semi-Markov Models -- 12.1. Introduction -- 12.2. Homogeneous semi-Markov process -- 12.3. Semi-Markov option model -- 12.4. Semi-Markov VaR models -- 12.5. Conclusion -- Chapter 13: Monte Carlo Semi-Markov Simulation Methods -- 13.1. Presentation of our simulation model -- 13.2. The semi-Markov Monte Carlo model in a homogeneous environment -- 13.3. A credit risk example -- 13.4. Semi-Markov Monte Carlo with initial recurrence backward time in homogeneous case -- 13.5. The SMMC applied to claim reserving problem
13.6. An example of claim reserving calculation -- Conclusion -- Bibliography -- Index
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 VaR Techniques. 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 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
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Janssen, Jacques Applied Diffusion Processes from Engineering to Finance Hoboken : John Wiley & Sons, Incorporated,c2013 9781118578339
主題 Business mathematics.;Differential equations, Partial.;Diffusion processes.;Engineering mathematics
Electronic books
Alt Author Manca, Oronzio
Manca, Raimondo
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