內容簡介
Science Press asked me to write a preface for their series of books called “Mathematics Monograph Series" . They told me that the Press had published nearly 30 mathematical monographs in this series since 2006. This reminded me that, also in 2006, I received an email message from the Editor in Chief of “Sugaku Tushin" ( "Mathematical Communications",the membership mag- azine of the Mathematical Society of Japan). The Editor in Chief told me that they were planning to have a special section on“Recent development in Chinese mathematical community", and invited me to write an article for the special section. As a result, 1 published in their magazine an article called “Some Aspects of Mathematical Community in China". Among other things, in the article I demonstrated that, with the favorable environment, the Chi- nese mathematical community had made great progress since the late 1970s (when China started to implement“Reform and Opening-up Policy”): A large number of publications (including articles and monographs) have been written by Chinese mathematicians, there have been always Chinese mathematicians presenting their speeches at various international academic conferences or workshops, many Chinese mathematicians have served as editors of interna- tional academic journals, or as members in various academic organizations. All these reveal that the Chinese mathematical community which has been growing rapidly has exerted more and more influence in the world.
圖書目錄
1 Foundation of Probability Theory and Discrete-Time Martingales
2 Portfolio Selection Theory in Discrete-Time
3 Financial Markets in Discrete Time
4 Martingale Theory and Ito Stochastic Analysis
5 The Black-Scholes Model and Its Modifications
6 Pricing and Hedging of Exotic Options
7 Ito Process and Diffusion Models
8 Term Structure Models for Interest Rates
9 Optimal Investment-Consumption Strategies in Diffusion Models
10 Static Risk Measures
11 Stochastic Calculus and Semimartingale Model
12 Optimal Investment in Incomplete Markets
13 Martingale Method for Utility Maximization
14 Optimal Growth Portfolios and Option Pricing
References
Index
4.3.3 Reflection Principle of Brownian Motion
4.3.4 Stochastic Exponentials and Novikov Theorem