학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #6
by 김재홍(KAIST)
This is part of an informal seminar series to be given by Mr. Jaehong Kim, who has been studying the book "Hodge theory and Complex Algebraic Geometry Vol 1 by Claire Voisin" for a few months. There will be 6-8 seminars during Spring 2024, and it will summarize about 70-80% of the book.
This presentation focuses on unbiased simulation methods for quantities associated with sample paths from stochastic differential equations. Unbiased simulation methods can be found by changing probability measures with appropriately selecting the Radon-Nikodym derivative processes. I propose an unbiased Monte-Carlo simulation method that can be used even when the Girsanov kernel for the change of probability measures is not bounded. Then, I illustrate its practical application through an example involving unbiased Monte Carlo simulation for pricing the continuously averaging arithmetic Asian options under the Black-Scholes model.
