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 StroockVaradhan martingale characterization of diffusions (Karlin and Taylor [KAR 81])  2.8. The FeynmanKac 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 BlackScholesSamuelson model  5.3. Pricing no plain vanilla calls with the BlackScholesSamuelson model  5.4. Zerocoupon pricing under the assumption of no arbitrage  Chapter 6: Exotic and American Options Pricing Theory  6.1. Introduction  6.2. The GarmanKohlhagen formula  6.3. Binary or digital options  6.4. "Asset or nothing" options  6.5. Numerical examples  6.6. Pathdependent options  6.7. Multiasset 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. LévyKhintchine formula  10.5. Examples of Lévy processes  10.6. Variance gamma (VG) process  10.7. The BrownianPoisson 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: SemiMarkov Models  12.1. Introduction  12.2. Homogeneous semiMarkov process  12.3. SemiMarkov option model  12.4. SemiMarkov VaR models  12.5. Conclusion  Chapter 13: Monte Carlo SemiMarkov Simulation Methods  13.1. Presentation of our simulation model  13.2. The semiMarkov Monte Carlo model in a homogeneous environment  13.3. A credit risk example  13.4. SemiMarkov 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 reallife problems. The authors point out the strict interrelations 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 semiMarkov 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: SemiMarkov Models. 13. Monte Carlo SemiMarkov 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 (EuroInstitut d'Actuariat, University of West Brittany, Brest, France) and TélécomBretagne (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

