LEADER 04767nam 22008295 450 001 9910958983203321 005 20250731074856.0 010 $a3-662-03620-7 024 7 $a10.1007/978-3-662-03620-4 035 $a(CKB)2660000000026255 035 $a(SSID)ssj0000855153 035 $a(PQKBManifestationID)11516675 035 $a(PQKBTitleCode)TC0000855153 035 $a(PQKBWorkID)10913132 035 $a(PQKB)10450518 035 $a(DE-He213)978-3-662-03620-4 035 $a(MiAaPQ)EBC3097703 035 $a(PPN)238080447 035 $a(EXLCZ)992660000000026255 100 $a20130125d1998 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic Differential Equations $eAn Introduction with Applications /$fby Bernt Oksendal 205 $a5th ed. 1998. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1998. 215 $a1 online resource (XIX, 324 p.) 225 1 $aUniversitext,$x2191-6675 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-63720-6 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- 2. Some Mathematical Preliminaries -- 3. Ito Integrals -- 4. The Ito Formula and the Martingale Representation Theorem -- 5. Stochastic Differential Equations -- 6. The Filtering Problem -- 7. Diffusions: Basic Properties -- 8. Other Topics in Diffusion Theory -- 9. Applications to Boundary Value Problems -- 10. Application to Optimal Stopping -- 11. Application to Stochastic Control -- 12. Application to Mathematical Finance -- Appendix A: Normal Random Variables -- Appendix B: Conditional Expectation -- Appendix C: Uniform Integrability and Martingale Convergence -- Appendix D: An Approximation Result -- Solutions and Additional Hints to Some of the Exercises -- References -- List of Frequently Used Notation and Symbols. 330 $aThe main new feature of the fifth edition is the addition of a new chapter, Chapter 12, on applications to mathematical finance. I found it natural to include this material as another major application of stochastic analysis, in view of the amazing development in this field during the last 10-20 years. Moreover, the close contact between the theoretical achievements and the applications in this area is striking. For example, today very few firms (if any) trade with options without consulting the Black & Scholes formula! The first 11 chapters of the book are not much changed from the previous edition, but I have continued my efforts to improve the presentation through­ out and correct errors and misprints. Some new exercises have been added. Moreover, to facilitate the use of the book each chapter has been divided into subsections. If one doesn't want (or doesn't have time) to cover all the chapters, then one can compose a course by choosing subsections from the chapters. The chart below indicates what material depends on which sections. Chapter 6 Chapter IO Chapter 12 For example, to cover the first two sections of the new chapter 12 it is recom­ mended that one (at least) covers Chapters 1-5, Chapter 7 and Section 8.6. VIII Chapter 10, and hence Section 9.1, are necessary additional background for Section 12.3, in particular for the subsection on American options. 410 0$aUniversitext,$x2191-6675 606 $aProbabilities 606 $aDifferential equations 606 $aMathematical physics 606 $aSystem theory 606 $aControl theory 606 $aMathematical optimization 606 $aCalculus of variations 606 $aProbability Theory 606 $aDifferential Equations 606 $aTheoretical, Mathematical and Computational Physics 606 $aSystems Theory, Control 606 $aCalculus of Variations and Optimization 615 0$aProbabilities. 615 0$aDifferential equations. 615 0$aMathematical physics. 615 0$aSystem theory. 615 0$aControl theory. 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 14$aProbability Theory. 615 24$aDifferential Equations. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aSystems Theory, Control. 615 24$aCalculus of Variations and Optimization. 676 $a519.2 686 $a60G40$2msc 686 $a60H10$2msc 686 $a60J45$2msc 700 $aOksendal$b Bernt$4aut$4http://id.loc.gov/vocabulary/relators/aut$0340540 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910958983203321 996 $aStochastic differential equations$9331338 997 $aUNINA