Uniqueness Of Solutions For Two Classes Of Cauchy Problem And Their Applications To Financial Mathematics

In this paper, we consider the well-posedness of the terminal value problems which interest rate derivative products satisfy when the interest rate is modeled by Vasicek model or C-I-R model. The main work is the follows.Firstly, by using the maximum principle, the Schauder interior estimates and constructing the proper auxiliary function, we proved the existence and uniqueness of the solutions to the terminal value problem which interest rate derivative products satisfy when the interest rate is modeled by Vasicek model.Secondly, by means of the maximum principle, the Schauder interior estimates, the approximation by smooth functions and establishing the approximate auxiliary functions, we also proved the existence and uniqueness of the solutions to the boundary value problem which interest rate derivative products satisfy , but the interest rate is modeled by C-I-R model.Finally, we demonstrate their applications to financial mathematics.