這門課程將涵蓋機率論、隨機過程、隨機微積分以及它們在各種衍生品評價中的應用。機率論將使學生理解隨機事件和機率分佈的基本概念，從而為後續的學習打下基礎。
隨機過程將介紹時間變化的隨機現象，例如布朗運動和隨機漫步，以及它們在金融市場中的應用。
隨機微積分將使學生瞭解如何對隨機過程進行微積分操作，並應用於金融衍生品的定價和風險管理。課程將強調理論知識與實際應用的結合，並通過案例研究和實際問題解決來加強學生的技能和理解。This course will cover probability theory, stochastic processes, stochastic calculus, and their applications in the evaluation of various derivatives. Probability theory will enable students to understand the basic concepts of random events and probability distribution, thereby laying the foundation for subsequent learning.
Stochastic Processes will introduce time-varying stochastic phenomena, such as Brownian motion and random walks, and their applications to financial markets.
Stochastic calculus will allow students to understand how to perform calculus operations on stochastic processes and apply them to the pricing and risk management of financial derivatives. The course will emphasize the integration of theoretical knowledge with practical application, and strengthen students' skills and understanding through case studies and practical problem solving.
1. Shreve, S.E., Stochastic Calculus for Finance II Continuous-Time Models, Springer-Verlag, NY, 2004. (Textbook)
2. Musiela, M. and Rutkowski, M., Martingale Methods in Financial Modelling, Springer-Verlag, NY, 1997. (Reference)
1. Shreve, S.E., Stochastic Calculus for Finance II Continuous-Time Models, Springer-Verlag, NY, 2004. (Textbook)
2. Musiela, M. and Rutkowski, M., Martingale Methods in Financial Modelling, Springer-Verlag, NY, 1997. (Reference)
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 期中考期中考 midterm exam |
50 | |
| 期末考期末考 final exam |
50 |
