I organize this seminar together with Claudiu Mîndrilă. It takes place every Monday at 11:00 in room number 307 at IMAR.
Seminar title: Brownian Motion to Black-Scholes Equation: A Seminar on Financial Mathematics
Objective: To provide a self-contained introduction to the concepts of Brownian motion and the Black-Scholes equation, with a focus on their applications in finance. We will mainly follow Stochastic Calculus for Finance II (Continuous-Time Models) by S.E. Shreve.
Key topics covered:
Rigorously construction of Brownian motion and a presentation of the key properties.
Introduction to the Black-Scholes equation, key assumptions, and applications in finance.
No prior knowledge of probabilities and statistics is required to attend the seminar.
Lecture 1: general Probability theory (speaker: Rares Stan)
Lecture 2: general Probability theory (speaker: Rares Stan)
Lecture 3: Law of Large Numbers and Central Limit Theorem (speakers: Mihai Pavel, Claudiu Mîndrilă)
Lecture 4: Conditional expectations (speaker: Rares Stan)
Lecture 5: Martingale (speaker: Rares Stan)
Lecture 6: Risk neutral measure I (speaker: Ionel Popescu)
Lecture 7: Risk neutral measure II (speaker: Ionel Popescu)
Lecture 8: Risk neutral measure III (speaker: Ionel Popescu)
Lecture 9: Introduction to Brownian Motion (speaker: Rares Stan)
Lecture 10: Weiner's construction of the Brownian Motion I (speaker: Claudiu Mîndrilă)
Lecture 11: Weiner's construction of the Brownian Motion II (speaker: Claudiu Mîndrilă)
Lecture 12: Hölder continuity (speaker: Claudiu Mîndrilă)
Lecture 13: Problem session
Lecture 14: Introduction into stochastic calculus (speaker: Claudiu Mîndrilă)
Lecture 15: Ito's integral (speaker: Claudiu Mîndrilă)