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Author:   Carlos A. Braumann
Publisher:   John Wiley & Sons Inc
Imprint:   John Wiley & Sons Inc
Dimensions:   Width: 15.80cm , Height: 2.00cm , Length: 23.10cm
Weight:   0.522kg
ISBN:  

9781119166061

ISBN 10:   1119166063
Pages:   304
Publication Date:   26 April 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Preface xi About the companion website xv 1 Introduction 1 2 Revision of probability and stochastic processes 9 2.1 Revision of probabilistic concepts 9 2.2 Monte Carlo simulation of random variables 25 2.3 Conditional expectations, conditional probabilities, and independence 29 2.4 A brief review of stochastic processes 35 2.5 A brief review of stationary processes 40 2.6 Filtrations, martingales, and Markov times 41 2.7 Markov processes 45 3 An informal introduction to stochastic differential equations 51 4 The Wiener process 57 4.1 Definition 57 4.2 Main properties 59 4.3 Some analytical properties 62 4.4 First passage times 64 4.5 Multidimensional Wiener processes 66 5 Diffusion processes 67 5.1 Definition 67 5.2 Kolmogorov equations 69 5.3 Multidimensional case 73 6 Stochastic integrals 75 6.1 Informal definition of the Itô and Stratonovich integrals 75 6.2 Construction of the Itô integral 79 6.3 Study of the integral as a function of the upper limit of integration 88 6.4 Extension of the Itô integral 91 6.5 Itô theorem and Itô formula 94 6.6 The calculi of Itô and Stratonovich 100 6.7 The multidimensional integral 104 7 Stochastic differential equations 107 7.1 Existence and uniqueness theorem and main proprieties of the solution 107 7.2 Proof of the existence and uniqueness theorem 111 7.3 Observations and extensions to the existence and uniqueness theorem 118 8 Study of geometric Brownian motion (the stochastic Malthusian model or Black–Scholes model) 123 8.1 Study using Itô calculus 123 8.2 Study using Stratonovich calculus 132 9 The issue of the Itô and Stratonovich calculi 135 9.1 Controversy 135 9.2 Resolution of the controversy for the particular model 137 9.3 Resolution of the controversy for general autonomous models 139 10 Study of some functionals 143 10.1 Dynkin’s formula 143 10.2 Feynman–Kac formula 146 11 Introduction to the study of unidimensional Itô diffusions 149 11.1 The Ornstein–Uhlenbeck process and the Vasicek model 149 11.2 First exit time from an interval 153 11.3 Boundary behaviour of Itô diffusions, stationary densities, and first passage times 160 12 Some biological and financial applications 169 12.1 The Vasicek model and some applications 169 12.2 Monte Carlo simulation, estimation and prediction issues 172 12.3 Some applications in population dynamics 179 12.4 Some applications in fisheries 192 12.5 An application in human mortality rates 201 13 Girsanov’s theorem 209 13.1 Introduction through an example 209 13.2 Girsanov’s theorem 213 14 Options and the Black–Scholes formula 219 14.1 Introduction 219 14.2 The Black–Scholes formula and hedging strategy 226 14.3 A numerical example and the Greeks 231 14.4 The Black–Scholes formula via Girsanov’s theorem 236 14.5 Binomial model 241 14.6 European put options 248 14.7 American options 251 14.8 Other models 253 15 Synthesis 259 References 269 Index 277

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Author Information

CARLOS A. BRAUMANN is Professor in the Department of Mathematics and member of the Research Centre in Mathematics and Applications, Universidade de Évora, Portugal. He is an elected member of the International Statistical Institute (since 1992), a former President of the European Society for Mathematical and Theoretical Biology (2009-12) and of the Portuguese Statistical Society (2006-09 and 2009-12), and a former member of the European Regional Committee of the Bernoulli Society (2008-12). He has dealt with stochastic differential equation (SDE) models and applications (mainly biological).

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