A Rigorous Proof of Fundamental Theorem of Uncertain Calculus

This paper revises the definition of the general Liu process via requiring its drift and diffusion to be sample-continuous. Then it is verified that almost all sample paths of the general Liu process are locally Lipschitz continuous. At last, a rigorous proof of fundamental theorem of uncertain calculus is given.

Pricing Convertible Bond in Uncertain Financial Market

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.