{"id":15578,"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=15578"},"modified":"2024-11-15T15:58:17","modified_gmt":"2024-11-15T07:58:17","slug":"%e8%b2%a1%e5%8b%99%e6%95%b8%e5%ad%b8%e5%b0%8e%e8%ab%96%e4%ba%8c-introduction-to-financial-mathematics-ii-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e6%85%b6%e5%a0%82%e8%80%81%e5%b8%ab","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-science\/am\/%e8%b2%a1%e5%8b%99%e6%95%b8%e5%ad%b8%e5%b0%8e%e8%ab%96%e4%ba%8c-introduction-to-financial-mathematics-ii-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e6%85%b6%e5%a0%82%e8%80%81%e5%b8%ab","title":{"rendered":"\u8ca1\u52d9\u6578\u5b78\u5c0e\u8ad6(\u4e8c) Introduction to Financial Mathematics II | \u61c9\u7528\u6578\u5b78\u7cfb \u5433\u6176\u5802\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"15578\" class=\"elementor elementor-15578\">\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 elementor-element-90a0113 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90a0113\" 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-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-78bf394\" data-id=\"78bf394\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\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_5559\" 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<div class=\"penci-ibox-stit\">Introduction to Financial Mathematics II <\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u8ca1\u52d9\u6578\u5b78\u5c0e\u8ad6(\u4e8c)<\/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        <div id=\"eael-advance-tabs-c6381f4\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"c6381f4\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                         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24zm96-192c13.3 0 24 10.7 24 24s-10.7 24-24 24-24-10.7-24-24 10.7-24 24-24zm128 368c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">\u8ab2\u7a0b\u7db1\u8981<\/span>                            \n                                                    <\/li>\n                                            <li id=\"calendar\" class=\"inactive eael-tab-item-trigger\" aria-selected=\"false\" data-tab=\"4\" role=\"tab\" tabindex=\"-1\" aria-controls=\"calendar-tab\" aria-expanded=\"false\">\n                            \n                                                                <svg class=\"e-font-icon-svg 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                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/span>                            \n                                                    <\/li>\n                                    <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p style=\"font-size: 16px;\">\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 \/>\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.<\/p><p>\u53c3\u8003\u7528\u66f8\uff1a<\/p><ol style=\"font-size: 14px;\"><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.\u00a0<\/li><\/ol><p><span style=\"font-size: 14px; color: #ff00ff;\">\u70ba\u6c42\u5b78\u7fd2\u6210\u6548\u5b8c\u7f8e\uff0c\u8acb\u8cfc\u8cb7\u8ab2\u672c\uff01<\/span><\/p><p>\u00a0<\/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\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u6559\u5e2b<\/span><\/span><\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u61c9\u7528\u6578\u5b78\u7cfb \u5433\u6176\u5802\u8001\u5e2b<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u5b78\u5206<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a03\u5b78\u5206<\/span><\/td><\/tr><tr><th class=\"text\" style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u5e74\u5ea6<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a099\u5b78\u5e74\u5ea6<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u6388\u8ab2\u5c0d\u8c61<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u78a9\u58eb\u73ed\u5b78\u751f<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u9810\u5099\u77e5\u8b58<\/span><\/span><\/th><td class=\"text\" bgcolor=\"#EEEEEE\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0\u5fae\u7a4d\u5206<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\"><span style=\"color: #313131; font-family: PT Serif, serif;\"><span style=\"font-weight: 400; white-space: normal;\">\u8ab2\u7a0b\u63d0\u4f9b<\/span><\/span><\/th><td class=\"text\"><span style=\"color: #313131; font-family: PT Serif, serif;\">\u00a0<a href=\"#video\">\u8ab2\u7a0b\u5f71\u97f3<\/a>\u00a0 \u00a0<a href=\"#syllabus\">\u8ab2\u7a0b\u7db1\u8981<\/a> \u00a0\u00a0<a href=\"#calendar\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/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-30\" class=\"tablepress tablepress-id-30\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/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=16007\">\u7dda\u4e0a\u89c0\u770b<\/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=16265\">\u7dda\u4e0a\u89c0\u770b<\/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=16277\">\u7dda\u4e0a\u89c0\u770b<\/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=16292\">\u7dda\u4e0a\u89c0\u770b<\/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=16319\">\u7dda\u4e0a\u89c0\u770b<\/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=16337\">\u7dda\u4e0a\u89c0\u770b<\/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=16361\">\u7dda\u4e0a\u89c0\u770b<\/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=16373\">\u7dda\u4e0a\u89c0\u770b<\/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=16407\">\u7dda\u4e0a\u89c0\u770b<\/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=16439\">\u7dda\u4e0a\u89c0\u770b<\/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=16505\">\u7dda\u4e0a\u89c0\u770b<\/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=16613\">\u7dda\u4e0a\u89c0\u770b<\/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=16631\">\u7dda\u4e0a\u89c0\u770b<\/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=16755\">\u7dda\u4e0a\u89c0\u770b<\/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=16817\">\u7dda\u4e0a\u89c0\u770b<\/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=16942\">\u7dda\u4e0a\u89c0\u770b<\/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=16959\">\u7dda\u4e0a\u89c0\u770b<\/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=16990\">\u7dda\u4e0a\u89c0\u770b<\/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=17057\">\u7dda\u4e0a\u89c0\u770b<\/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=17104\">\u7dda\u4e0a\u89c0\u770b<\/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=17232\">\u7dda\u4e0a\u89c0\u770b<\/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=17238\">\u7dda\u4e0a\u89c0\u770b<\/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=17244\">\u7dda\u4e0a\u89c0\u770b<\/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=17250\">\u7dda\u4e0a\u89c0\u770b<\/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=17256\">\u7dda\u4e0a\u89c0\u770b<\/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=17262\">\u7dda\u4e0a\u89c0\u770b<\/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=17268\">\u7dda\u4e0a\u89c0\u770b<\/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=17274\">\u7dda\u4e0a\u89c0\u770b<\/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=17280\">\u7dda\u4e0a\u89c0\u770b<\/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=17286\">\u7dda\u4e0a\u89c0\u770b<\/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=17292\">\u7dda\u4e0a\u89c0\u770b<\/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=17298\">\u7dda\u4e0a\u89c0\u770b<\/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=17304\">\u7dda\u4e0a\u89c0\u770b<\/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=17310\">\u7dda\u4e0a\u89c0\u770b<\/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=17316\">\u7dda\u4e0a\u89c0\u770b<\/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=17322\">\u7dda\u4e0a\u89c0\u770b<\/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=17328\">\u7dda\u4e0a\u89c0\u770b<\/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=17334\">\u7dda\u4e0a\u89c0\u770b<\/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=17340\">\u7dda\u4e0a\u89c0\u770b<\/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=17346\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-30 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>\/*! 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