{"id":15692,"date":"2022-08-18T09:45:21","date_gmt":"2022-08-18T01:45:21","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=15692"},"modified":"2022-08-18T13:52:01","modified_gmt":"2022-08-18T05:52:01","slug":"introduction-to-financial-mathematics-ii-department-of-applied-mathematics-prof-ching-tang-wu","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-financial-mathematics-ii-department-of-applied-mathematics-prof-ching-tang-wu","title":{"rendered":"Introduction to Financial Mathematics II | Department of Applied Mathematics Prof. Ching-Tang Wu"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"15692\" class=\"elementor elementor-15692\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element 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href=\"https:\/\/ocw.nycu.edu.tw\/\">Homepage<\/a><\/span><\/span><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-0025485 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0025485\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-0446ed9\" data-id=\"0446ed9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f5840a elementor-widget elementor-widget-penci-info-box\" data-id=\"2f5840a\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_48932\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t\t\t\t\t\t<h3 class=\"penci-ibox-title\">Introduction to Financial Mathematics II <\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6381f4 elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"c6381f4\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t       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\/><\/style><\/p><p>\u672c\u8ab2\u7a0b\u662f\u7531\u4ea4\u901a\u5927\u5b78<a href=\"https:\/\/www.math.nycu.edu.tw\/\" data-cke-saved-href=\"http:\/\/www.math.nctu.edu.tw\/\">\u61c9\u7528\u6578\u5b78\u7cfb<\/a>\u63d0\u4f9b\u3002<br \/><br \/>\u672c\u8ab2\u7a0b\u4e3b\u8981\u8b93\u5b78\u751f\u4e86\u89e3\u4e26\u719f\u6089\u7814\u7a76\u8ca1\u52d9\u91d1\u878d\u65b9\u9762\u6240\u9700\u4e4b\u6578\u5b78\u5de5\u5177\u3002<br \/><br \/>\u8ab2\u7a0b\u7528\u66f8\uff1aS. E. Shreve: Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.<br \/><br \/>\u53c3\u8003\u7528\u66f8\uff1a<\/p><ol><li>T. M. Apostol: Mathematical Analysis, Second Edition<\/li><li>M. Baxter and A. Rennie: Financial Calculus.<\/li><li>T. Bj\u00f6rk: Arbitrage Theory in Continuous Time.<\/li><li>K. L. Chung: A Course in Probability Theory, Second Edition.<\/li><li>F. Delbaen and W. Schachermayer: The Mathematics of Arbitrage.<\/li><li>J. Elstrodt: Ma\u03b2- und Integrationstheorie, Third Edition.<\/li><li>H. F\u00f6llmer and A. Schied: Stochastic Finance. An Introduction in Discrete Time.<\/li><li>J. Jacod and Ph. Protter: Probability Essentials.<\/li><li>J. C. Hull: Options, Futures, &amp; Other Derivatives, Sixth Edition.<\/li><li>I. Karatzas: Lectures on the Mathematics of Finance.<\/li><li>I. Karatzas and S. E. Shreve: Brownian Motion and Stochastic Calculus, Second\u00a0 Edition.<\/li><li>I. Karatzas and S. E. Shreve: Method of Mathematical Finance.<\/li><li>D. Lamberton and B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance.<\/li><li>B. \u00d8ksendal: Stochastic Differential Equations, An Introduction with Applications,Sixth Edition.<\/li><li>R. T. Rockafellar: Convex Analysis.<\/li><li>H. L. Royden: Real Analysis, Third Edition.<\/li><li>A.N. Shiryaev: Probability Theory, Second Edition.<\/li><li>S. E. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model.<\/li><li>R. L. Wheeden and A. Zygmund: Measure and integral.<\/li><\/ol><p><span style=\"color: #ff00ff;\">\u70ba\u6c42\u5b78\u7fd2\u6210\u6548\u5b8c\u7f8e\uff0c\u8acb\u8cfc\u8cb7\u8ab2\u672c\uff01<\/span><\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\">Instructor(s)<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Department of Applied Mathematics Prof. Ching-Tang Wu<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Course Credits<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03 Credits<\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Academic Year<\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a099 Academic Year<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Level<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Graduate Students<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Prior Knowledge<\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0Calculus<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Related Resources<\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">Course Video<\/a>\u00a0 \u00a0<a href=\"#syllabus\">Course Syllabus<\/a>\u00a0 \u00a0<a href=\"#calendar\">Course Calendar<\/a><\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-31\" class=\"tablepress tablepress-id-31\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u4e03 Coutinuous-time Martingales<br \/>\n7.1 Stochastic process (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17352&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.1 Stochastic process (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17357&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.2 Uniform integrability<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17363&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.3 Martingale theory in continuous-time<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17369&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.4 Local martingales<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17375&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.5 Doob-Meyer decomposition<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17381&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">7.6 Semimartingales<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17387&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u516b Brownian Motions<br \/>\n8.1 Scaled random walk<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17393&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">8.2 Brownian motions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17399&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">8.3 The Brownian sample paths<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17405&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">8.4 Exponential martingales<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17411&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">8.5 d-dimensional Brownian motions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17417&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u4e5d Stochastic Integrals<br \/>\n9.1 Construction of stochastic integrals with respect to martingales (1\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17423&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.1 Construction of stochastic integrals with respect to martingales (2\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17429&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.1 Construction of stochastic integrals with respect to martingales (3\/3)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17435&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.2 Stochastic integrals with respect to semimartingales<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17441&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.3 Stochastic integrals with respect to local martingales<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17447&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.4 It\u00f4 formula  (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17453&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.4 It\u00f4 formula  (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17459&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.5 Integration by parts<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17465&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.6 Martingale representation theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17471&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.7 Change of Measures<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17477&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.8 Girsanov theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17483&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">9.9 Local times<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17489&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u5341 Stochastic Differential Equations<br \/>\n10.1 Examples and some solution methods (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17495&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">10.1 Examples and some solution methods (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17501&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">10.2 An existence and uniqueness result<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17507&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">10.3 Weak and strong solutions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17513&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">10.4 Feynman-Kac theorem<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17519&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u5341\u4e00 Continuous-Time Models<br \/>\n11.1 Market portfolios and arbitrage<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17525&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">11.2 Equivalent local martingale measures<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17531&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">11.3 Completeness<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17537&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-34 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">11.4 Pricing for attainable contingent claim<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17543&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-35 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">11.5 Black-Scholes-Merton formula<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17549&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-36 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">11.6 The Greeks<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17555&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-37 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">11.7 Parity rrelations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17561&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-38 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u55ae\u5143\u5341\u4e8c Hedging<br \/>\n12.1 Hedging strategy for the simple contingent claim <br \/>\n12.2 Delta and gamma hedging<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17567&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-39 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix F\u3001Characteristic Functions<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17573&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-40 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix G\u3001Differntial Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17579&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-41 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">Appendix H\u3001Convex Analysis<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=17585&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-31 from cache --><\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">\u672c\u8ab2\u7a0b\u4e3b\u8981\u8b93\u5b78\u751f\u4e86\u89e3\u4e26\u719f\u6089\u7814\u7a76\u8ca1\u52d9\u91d1\u878d\u65b9\u9762\u6240\u9700\u4e4b\u6578\u5b78\u5de5\u5177\u3002<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong> \u4e3b\u984c\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e03 Continuous-Time Martingales<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">7.1 Stochastic processes<br \/>7.2 Uniform integrability<br \/>7.3 Martingale theory in continuous-time<br \/>7.4 Local martingales<br \/>7.5 Doob-Meyer decomposition<br \/>7.6 Semimartingales<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516b Brownian Motions<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">8.1 Scaled random walk<br \/>8.2 Brownian motions<br \/>8.3 The Brownian sample paths<br \/>8.4 Exponential martingales<br \/>8.5 d-dimensional Brownian motions<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e5d Stochastic Integrals<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">9.1 Construction of stochastic integrals with respect to martingales<br \/>9.2 Stochastic integrals with respect to semimartingales<br \/>9.3 It\u00f4 formula<br \/>9.4 Integration by parts<br \/>9.5 Martingale representation theorem<br \/>9.6 Girsanov theorem<br \/>9.7 Local times<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u5341 Stochastic Differential Equations<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">10.1 Examples and some solution methods<br \/>10.2 An existence and uniqueness result<br \/>10.3 Weak and strong solutions<br \/>10.4 Feynman-Kac theorem<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u5341\u4e00 Continuous-Time Models<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">11.1 Market portfolios and arbitrage<br \/>11.2 Equivalent local martingale measures<br \/>11.3 Completeness<br \/>11.4 Pricing for attainable contingent claim<br \/>11.5 Black-Scholes-Merton formula<br \/>11.6 Parity relations<br \/>11.7 The greeks<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u5341\u4e8c Hedging<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">12.1 Hedging strategy for the simple contingent claim<br \/>12.2 Delta and gamma hedging<br \/>12.3 Superhedging<br \/>12.4 Quantile hedging<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u516d Volatility<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">13.1 Historical volatility<br \/>13.2 Implied volatility<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Appendix<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">F . Convex Analysis<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">S. E. Shreve: Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.<\/p><p class=\"text\"><strong>\u53c3\u8003\u66f8\u76ee<\/strong><\/p><p class=\"text\">T. M. Apostol: Mathematical Analysis, Second Edition<br \/>M. Baxter and A. Rennie: Financial Calculus.<br \/>T. Bj\u00f6rk: Arbitrage Theory in Continuous Time.<br \/>K. L. Chung: A Course in Probability Theory, Second Edition.<br \/>F. Delbaen and W. Schachermayer: The Mathematics of Arbitrage.<br \/>J. Elstrodt: Ma\u03b2- und Integrationstheorie, Third Edition.<br \/>H. F\u00f6llmer and A. Schied: Stochastic Finance. An Introduction in Discrete Time.<br \/>J. Jacod and Ph. Protter: Probability Essentials.<br \/>J. C. Hull: Options, Futures, &amp; Other Derivatives, Sixth Edition.<br \/>I. Karatzas: Lectures on the Mathematics of Finance. I. Karatzas and S. E. Shreve: Brownian Motion and Stochastic Calculus, Second Edition.<br \/>I. Karatzas and S. E. Shreve: Method of Mathematical Finance.<br \/>D. Lamberton and B. Lapeyre: Introduction to Stochastic Calculus Applied to Finance.<br \/>B. \u00d8ksendal: Stochastic Differential Equations, An Introduction with Applications,Sixth Edition.<br \/>R. T. Rockafellar: Convex Analysis.<br \/>H. L. Royden: Real Analysis, Third Edition.<br \/>A.N. Shiryaev: Probability Theory, Second Edition.<br \/>S. E. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model.<br \/>R. L. Wheeden and A. Zygmund: Measure and integral.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u5e73\u6642\u6210\u7e3e(\u4f5c\u696d)<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">40%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u671f\u4e2d\u8003<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">30%<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u671f\u672b\u8003 <\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">30%<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4; font-size: 15px;\">\u672c\u8ab2\u7a0b\u884c\u4e8b\u66c6\u63d0\u4f9b\u8ab2\u7a0b\u9032\u5ea6\u8207\u8003\u8a66\u8cc7\u8a0a\u53c3\u8003\u3002<\/span><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong> \u7ae0\u7bc0<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong> \u4e3b\u984c\u5167\u5bb9<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e03 Continuous-Time Martingales<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">7.1 Stochastic processes<br \/>7.2 Uniform integrability<br \/>7.3 Martingale theory in continuous-time<br \/>7.4 Local martingales<br \/>7.5 Doob-Meyer decomposition<br \/>7.6 Semimartingales<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u516b Brownian Motions<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">8.1 Scaled random walk<br \/>8.2 Brownian motions<br \/>8.3 The Brownian sample paths<br \/>8.4 Exponential martingales<br \/>8.5 d-dimensional Brownian motions<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u4e5d Stochastic Integrals<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">9.1 Construction of stochastic integrals with respect to martingales<br \/>9.2 Stochastic integrals with respect to semimartingales<br \/>9.3 It\u00f4 formula<br \/>9.4 Integration by parts<br \/>9.5 Martingale representation theorem<br \/>9.6 Girsanov theorem<br \/>9.7 Local times<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u55ae\u5143\u5341 Stochastic Differential Equations<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">10.1 Examples and some solution methods<br \/>10.2 An existence and uniqueness result<br \/>10.3 Weak and strong solutions<br \/>10.4 Feynman-Kac theorem<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u55ae\u5143\u5341\u4e00 Continuous-Time Models<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">11.1 Market portfolios and arbitrage<br \/>11.2 Equivalent local martingale measures<br \/>11.3 Completeness<br \/>11.4 Pricing for attainable contingent claim<br \/>11.5 Black-Scholes-Merton formula<br \/>11.6 Parity relations<br \/>11.7 The greeks<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        <\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d7723a8 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"d7723a8\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 var(--divider-element-spacing);flex-shrink:0}.elementor-widget-divider .elementor-icon{font-size:var(--divider-icon-size)}.elementor-widget-divider .elementor-divider-separator{display:flex;margin:0;direction:ltr}.elementor-widget-divider--view-line_icon .elementor-divider-separator,.elementor-widget-divider--view-line_text .elementor-divider-separator{align-items:center}.elementor-widget-divider--view-line_icon 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class=\"elementor-item\" tabindex=\"-1\">College of Engineering Bioscience<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5379\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-humanities-and-social-sciences\" class=\"elementor-item\" tabindex=\"-1\">College of Humanities Arts and Social Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5378\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-hakka-affair-culture\" class=\"elementor-item\" tabindex=\"-1\">College of Hakka Affair Culture<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118070\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\" tabindex=\"-1\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Introduction t&hellip;<\/p>\n","protected":false},"featured_media":17596,"parent":5277,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":{"footnotes":""},"categories":[242],"tags":[341,345,347,986],"class_list":["post-15692","course_page","type-course_page","status-publish","format-standard","has-post-thumbnail","hentry","category-department-of-applied-mathematics-en","tag-label-all-course-en","tag-label-college-of-science-en","tag-label-am-en","tag-label-introduction-to-financial-mathematics-ii-99-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Introduction to Financial Mathematics II | Department of Applied Mathematics 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