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These studies are available for the following degree students:</p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Master's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master's Degree Programme in Mathematics&nbsp;(Subject Teacher)</li><li>Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Doctoral Programme in Mathematics and Statistics</li><li>Doctoral Programme in Mathematics and Science (Specialication in Mathematics)</li><br></ul>","fi":"<p>Tämä opintojakso on tarjolla Matematiikan syventävät opinnot -ristiinopiskeluverkostossa. Verkoston opinnot ovat tarjolla seuraaville opiskelijoille:</p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajien kandidaattiohjelma</li><li>Matematiikan aineenopettajien maisteriohjelma</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan kandidaattiohjelma (matematiikan opintosuunta)</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan maisteriiohjelma (matematiikan opintosuunta)</li><li>Matematiikan ja tilastotieteen tohtoriohjelma</li><li>Matemaattisten tieteiden ja luonnontieteiden tohtoriohjelma (matematiikan opintosuunta)</li><br></ul>"},"cooperationNetwork":{"abbreviation":"matematiikansyventavat","name":{"en":"Cross-institutional studies in advanced courses in mathematics and statistics","fi":"Matematiikan ja tilastotieteen syventävien kurssien ristiinopiskelu","sv":"Korsstudier i fördjupade kurser i matematik och statistik"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"Learning objectives are:\r\n- the theory for multiperiod (discrete time) stochastic models and their properties and usage in financial applications \r\n- the theory of optimal stopping (discrete time)  and its application in pricing American options\r\n- basic poperties of Brownian motion and Ito&#39;s formula\r\n- the theory of the Black-Scholes model and pricing of European options","fi":"Att lära deltagarna:\r\n- teorin av multiperiodiska (diskret tid) stokastiska modeller och deras egenskaper samt  använding inom  finansiella tillämpningar \r\n- teorin av optimal stopping (diskret tid) och dess användning för prissättandet av amerikanska optioner\r\n- grundläggande egenskaper hos brownska rörelsen och Itos formel \r\n- teorin för Black-Scholes formel och prissättandet av  europeiska optioner","sv":"Att lära deltagarna:\r\n- teorin av multiperiodiska (diskret tid) stokastiska modeller och deras egenskaper samt  använding inom  finansiella tillämpningar \r\n- teorin av optimal stopping (diskret tid) och dess användning för prissättandet av amerikanska optioner\r\n- grundläggande egenskaper hos brownska rörelsen och Itos formel \r\n- teorin för Black-Scholes formel och prissättandet av  europeiska optioner"},"tweetText":null,"content":{"en":"Contents of the course:\r\n- discrete time multiperiod model: self financing strategies,  arbitrage, completeness, European contingent claims (discrete time).\r\n- American contingent claims (discrete time) : martingales,  optimal stopping, \r\n- Black-Scholes model: Brownian motion and Ito&#39;s formula, European options; pricing and hedging","fi":"Kursens innehåll:\r\n- multiperiodiska modeller i diskret tid: self finansierade strategier, arbitrage, fullständighet, Europeiska betingade (contingent)  krav. \r\n- Amerikanska betingade (contingent)  krav: martingaler , optimal stopping, \r\n- Black-Scholes model: Brownska rörelsen och Ito&#39;s formel, Europeiska optioner; prissättande och skyddstrategier","sv":"Kursens innehåll:\r\n- multiperiodiska modeller i diskret tid: self finansierade strategier, arbitrage, fullständighet, Europeiska betingade (contingent)  krav. \r\n- Amerikanska betingade (contingent)  krav: martingaler , optimal stopping, \r\n- Black-Scholes model: Brownska rörelsen och Ito&#39;s formel, Europeiska optioner; prissättande och skyddstrategier"},"additional":{"en":"The course may be lectured more seldom than every second year","sv":"Kursen ges kanske mera sällan än vartannat år"},"prerequisites":{"en":"BSc level analysis, calculus and probability theory","sv":"Analys del I 272021\r\nAnalys del II 272022\r\nFlerdimensionell analys del I 272023\r\nFlerdimensionell analys del II 272024\r\nSannolikhetslära del I, 272026.0\r\nSannolikhetslära del II, 272027.0"},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Financial Mathematics","id":"otm-5315bc80-aac7-32fa-990e-14871cbfe88b","code":"MA00BD35","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-5a6a3701-b188-3724-9476-784e433a4d92"],"organisations":[],"attainmentLanguages":["en","sv"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}