10.3 Weak and strong solutions
| Week | Course Content | Course Video |
|---|---|---|
| 單元七 Coutinuous-time Martingales 7.1 Stochastic process (1/2) | Watch Online | |
| 7.1 Stochastic process (2/2) | Watch Online | |
| 7.2 Uniform integrability | Watch Online | |
| 7.3 Martingale theory in continuous-time | Watch Online | |
| 7.4 Local martingales | Watch Online | |
| 7.5 Doob-Meyer decomposition | Watch Online | |
| 7.6 Semimartingales | Watch Online | |
| 單元八 Brownian Motions 8.1 Scaled random walk | Watch Online | |
| 8.2 Brownian motions | Watch Online | |
| 8.3 The Brownian sample paths | Watch Online | |
| 8.4 Exponential martingales | Watch Online | |
| 8.5 d-dimensional Brownian motions | Watch Online | |
| 單元九 Stochastic Integrals 9.1 Construction of stochastic integrals with respect to martingales (1/3) | Watch Online | |
| 9.1 Construction of stochastic integrals with respect to martingales (2/3) | Watch Online | |
| 9.1 Construction of stochastic integrals with respect to martingales (3/3) | Watch Online | |
| 9.2 Stochastic integrals with respect to semimartingales | Watch Online | |
| 9.3 Stochastic integrals with respect to local martingales | Watch Online | |
| 9.4 Itô formula (1/2) | Watch Online | |
| 9.4 Itô formula (2/2) | Watch Online | |
| 9.5 Integration by parts | Watch Online | |
| 9.6 Martingale representation theorem | Watch Online | |
| 9.7 Change of Measures | Watch Online | |
| 9.8 Girsanov theorem | Watch Online | |
| 9.9 Local times | Watch Online | |
| 單元十 Stochastic Differential Equations 10.1 Examples and some solution methods (1/2) | Watch Online | |
| 10.1 Examples and some solution methods (2/2) | Watch Online | |
| 10.2 An existence and uniqueness result | Watch Online | |
| 10.3 Weak and strong solutions | Watch Online | |
| 10.4 Feynman-Kac theorem | Watch Online | |
| 單元十一 Continuous-Time Models 11.1 Market portfolios and arbitrage | Watch Online | |
| 11.2 Equivalent local martingale measures | Watch Online | |
| 11.3 Completeness | Watch Online | |
| 11.4 Pricing for attainable contingent claim | Watch Online | |
| 11.5 Black-Scholes-Merton formula | Watch Online | |
| 11.6 The Greeks | Watch Online | |
| 11.7 Parity rrelations | Watch Online | |
| 單元十二 Hedging 12.1 Hedging strategy for the simple contingent claim 12.2 Delta and gamma hedging | Watch Online | |
| Appendix F、Characteristic Functions | Watch Online | |
| Appendix G、Differntial Equations | Watch Online | |
| Appendix H、Convex Analysis | Watch Online |
COURSE
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