Jacques Janssen, Oronzio Manca, Raimondo Manca

Applied Diffusion Processes from Engineering to Finance (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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. 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. L vy 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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 416
• Erscheinungstermin: 8. April 2013
• Englisch
• ISBN-13: 9781118578346
• Artikelnr.: 38003338

Autorenporträt

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.

Inhaltsangabe

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 Itô's formula 19 2.3 Stochastic differential
equations (SDE) 24 2.4 Itô and diffusion processes 28 2.5 Some particular
cases of diffusion processes 32 2.6 Multidimensional diffusion processes 36
2.7 The Stroock-Varadhan martingale characterization of diffusions (Karlin
and Taylor) 41 2.8 The Feynman-Kac 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 3.2 Solving the heat equation 51 3.3
Solution by the method of Laplace transform 65 3.4 Green's functions 75
Chapter 4 Problems in Finance 85 4.1 Basic stochastic models for stock
prices 85 4.2 The bond investments 90 4.3 Dynamic deterministic continuous
time model for instantaneous interest rate 93 4.4 Stochastic continuous
time dynamic model for instantaneous interest rate 98 4.5 Multidimensional
Black and Scholes model 110 Chapter 5 Basic PDE in Finance 111 5.1
Introduction to option theory 111 5.2 Pricing the plain vanilla call with
the Black-Scholes-Samuelson model 115 5.3 Pricing no plain vanilla calls
with the Black-Scholes-Samuelson model 120 5.4 Zero-coupon pricing under
the assumption of no arbitrage 127 Chapter 6 Exotic and American Options
Pricing Theory 145 6.1 Introduction 145 6.2 The Garman-Kohlhagen formula
146 6.3 Binary or digital options 149 6.4 "Asset or nothing" options 150
6.5 Numerical examples 152 6.6 Path-dependent options 153 6.7 Multi-asset
options 157 6.8 American options 165 Chapter 7 Hitting Times for Diffusion
Processes and Stochastic Models in Insurance 177 7.1 Hitting or first
passage times for some diffusion processes 177 7.2 Merton's model for
default risk 193 7.3 Risk diffusion models for insurance 201 Chapter 8
Numerical Methods 219 8.1 Introduction 219 8.2 Discretization and numerical
differentiation 220 8.3 Finite difference methods 222 9.1 Nonlinear model
in heat conduction 232 Chapter 9 Advanced Topics in Engineering: Nonlinear
Models 231 9.2 Integral method applied to diffusive problems 233 9.3
Integral method applied to nonlinear problems 239 9.4 Use of
transformations in nonlinear problems 243 Chapter 10 Lévy Processes 255
10.1 Motivation 255 10.2 Notion of characteristic functions 257 10.3 Lévy
processes 257 10.4 Lévy-Khintchine formula 259 10.5 Examples of Lévy
processes 261 10.6 Variance gamma (VG) process 264 10.7 The
Brownian-Poisson model with jumps 266 10.8 Risk neutral measures for Lévy
models in finance 275 10.9 Conclusion 276 Chapter 11 Advanced Topics in
Insurance: Copula Models and VaR Techniques 277 11.1 Introduction 277 11.2
Sklar theorem (1959) 279 11.3 Particular cases and Fréchet bounds 280 11.4
Dependence 288 11.5 Applications in finance: pricing of the bivariate
digital put option 293 11.6 VaR application in insurance 296 Chapter 12
Advanced Topics in Finance: Semi-Markov Models 307 12.1 Introduction 307
12.2 Homogeneous semi-Markov process 308 12.3 Semi-Markov option model 328
12.4 Semi-Markov VaR models 332 12.5 Conclusion 339 Chapter 13 Monte Carlo
Semi-Markov Simulation Methods 341 13.1 Presentation of our simulation
model 341 13.2 The semi-Markov Monte Carlo model in a homogeneous
environment 345 13.3 A credit risk example 350 13.4 Semi-Markov Monte Carlo
with initial recurrence backward time in homogeneous case 362 13.5 The SMMC
applied to claim reserving problem 363 13.6 An example of claim reserving
calculation 366 Conclusion 379 Bibliography 381 Index 393