Applied diffusion processes from engineering to finance
 Responsibility
 Jacques Janssen, Oronzio Manca, Raimondo Manca.
 Language
 English.
 Publication
 London : ISTE Ltd ; Hoboken, NJ : John Wiley & Sons, Inc., [2013].
 Physical description
 xv, 391 pages : illustrations ; 25 cm.
 Series
 Applied stochastic methods series.
Access
Available online
 dx.doi.org Wiley Online Library
Math & Statistics Library
Stacks
Call number  Status 

QA274.75 .J36 2013  Unknown 
More options
Creators/Contributors
 Author/Creator
 Janssen, Jacques, 1939 author.
 Contributor
 Manca, Oronzio, author.
 Manca, Raimondo, author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 381391) and index.
 Contents

 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 Ito's formula 19 2.3 Stochastic differential equations (SDE) 24 2.4 Ito 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 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 BlackScholesSamuelson model 115 5.3 Pricing no plain vanilla calls with the BlackScholesSamuelson model 120 5.4 Zerocoupon pricing under the assumption of no arbitrage 127 Chapter 6 Exotic and American Options Pricing Theory 145 6.1 Introduction 145 6.2 The GarmanKohlhagen formula 146 6.3 Binary or digital options 149 6.4 "Asset or nothing" options 150 6.5 Numerical examples 152 6.6 Pathdependent options 153 6.7 Multiasset 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 Levy Processes 255 10.1 Motivation 255 10.2 Notion of characteristic functions 257 10.3 Levy processes 257 10.4 LevyKhintchine formula 259 10.5 Examples of Levy processes 261 10.6 Variance gamma (VG) process 264 10.7 The BrownianPoisson model with jumps 266 10.8 Risk neutral measures for Levy 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 Frechet 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: SemiMarkov Models 307 12.1 Introduction 307 12.2 Homogeneous semiMarkov process 308 12.3 SemiMarkov option model 328 12.4 SemiMarkov VaR models 332 12.5 Conclusion 339 Chapter 13 Monte Carlo SemiMarkov Simulation Methods 341 13.1 Presentation of our simulation model 341 13.2 The semiMarkov Monte Carlo model in a homogeneous environment 345 13.3 A credit risk example 350 13.4 SemiMarkov 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.
 (source: Nielsen Book Data)
 Publisher's 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 reallife problems in these three topics. 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 get the solutions of the different problems presented in the book. Advanced topics such as nonlinear problems, Levy processes and semiMarkov models in interactions with the diffusion models are discussed, as well as possible future interactions among Engineering, Finance and Insurance.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Applied stochastic methods series
 ISBN
 9781848212497
 1848212496