Financial Mathematics

Author: Li Xiangke
Publisher:
Publish Date: 2004-06-01
Features: From the perspective of international development trends, some mathematical problems in financial research have become quite advanced. This book focuses on asset pricing, demonstrating how to use mathematical methods to address financial issues. Chapter 1 covers fundamental mathematical content, including linear algebra, simple optimization methods and model building, as well as the mathematical interpretation of utility functions. Chapter 2 discusses risk preferences and stochastic dominance. This is the foundation of pricing theory, and many assumptions in subsequent mathematical models stem from it. The goal is to give readers a preliminary understanding of concepts like risk preferences from a mathematical perspective. Chapters 3 to 5 present three representative modern investment theory models that emerged after the 1950s, including the Markowitz mean-variance model, CAPM, and APT. Here, a "semi-mathematical" approach is adopted, providing detailed explanations from a mathematical viewpoint on the assumptions, derivation processes, related conclusions, and proofs of theorems for these models. Chapter 6 deals with continuous-time financial problems. The content is relatively "modern" and uses a purely mathematical approach. Readers will encounter advanced mathematics in this section. This book can serve as a textbook for university students majoring in finance and economics, particularly those in financial fields. It can also be used as a reference for researchers with basic mathematical knowledge who wish to further explore the application of mathematics in finance.