Stochastic Differential Equations: An Introduction with ApplicationsSpringer Science & Business Media, 15 de jul. de 2003 - 360 páginas This edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new exercises (without solutions) have beed added. They have all been placed in the end of each chapter, in order to facilitate the use of this edition together with previous ones. Several errors have been corrected and formulations have been improved. This has been made possible by the valuable comments from (in alphabetical order) Jon Bohlin, Mark Davis, Helge Holden, Patrick Jaillet, Chen Jing, Natalia Koroleva,MarioLefebvre,Alexander Matasov,Thilo Meyer-Brandis, Keigo Osawa, Bjørn Thunestvedt, Jan Ubøe and Yngve Williassen. I thank them all for helping to improve the book. My thanks also go to Dina Haraldsson, who once again has performed the typing and drawn the ?gures with great skill. Blindern, September 2002 Bernt Øksendal xv Preface to Corrected Printing, Fifth Edition The main corrections and improvements in this corrected printing are from Chapter 12. I have bene'tted from useful comments from a number of p- ple, including (in alphabetical order) Fredrik Dahl, Simone Deparis, Ulrich Haussmann, Yaozhong Hu, Marianne Huebner, Carl Peter Kirkebø, Ni- lay Kolev, Takashi Kumagai, Shlomo Levental, Geir Magnussen, Anders Øksendal, Jur ̈ gen Pottho?, Colin Rowat, Stig Sandnes, Lones Smith, S- suo Taniguchi and Bjørn Thunestvedt. I want to thank them all for helping me making the book better. I also want to thank Dina Haraldsson for pro'cient typing. |
Conteúdo
6 | 78 |
Mathematical Finance | 108 |
The Markov Property | 121 |
3 | 141 |
Itô Integrals | 148 |
Exercises | 166 |
43 | 177 |
Exercises | 237 |
Application to Mathematical Finance | 269 |
5 | 310 |
Normal Random Variables | 315 |
Uniform Integrability and Martingale | 323 |
Solutions and Additional Hints to Some of the Exercises | 331 |
References | 363 |
List of Frequently Used Notation and Symbols | 373 |
Application to Stochastic Control | 243 |
Outras edições - Ver todos
Stochastic Differential Equations: An Introduction with Applications Bernt Øksendal Visualização parcial - 2010 |
Stochastic Differential Equations: An Introduction with Applications Bernt Oksendal Prévia não disponível - 2010 |
Stochastic Differential Equations: An Introduction with Applications Bernt Øksendal Prévia não disponível - 2003 |
Termos e frases comuns
1-dimensional Brownian motion admissible portfolio arbitrage assume Borel bounded Bt be 1-dimensional Chapter choose condition constant continuous function Corollary define Definition denotes Dirichlet problem Dynkin's formula equation dXt Es,x Example Exercise exists filtering problem geometric Brownian motion Girsanov theorem given Hence Hint inf{t Itô diffusion Itô formula Itô integral Itô process Itô's formula L²(P Lemma Let f Let Xt linear lower semicontinuous market X(t Markov control Markov property martingale w.r.t. measurable function o-algebra obtain Øksendal optimal control optimal stopping optimal stopping problem Poisson problem process Xt Proof prove random variable satisfies solution solve stochastic differential equation stochastic process superharmonic supermeanvalued Suppose T-claim unique Xt)dt მე მყ