求积元法在金融工程计算领域应用初探

A Preliminary Study on the Application of QEM in Financial Engineering Analysis

金融工程领域的大量实际问题最终都可归结为对随机微分方程(组)的求解.针对金融工程计算领域涉及到的静态一维问题,首次将求积元方法应用于非自伴随微分方程的求解.建立了相应的求积元方法计算单元.对典型问题进行计算,并与解析解、有限差分解、有限元解分别进行对比.结果表明,求积元法是一种简单准确高效的数值方法,可进一步用于金融工程计算领域动态问题、二维问题的计算分析.

Many practical problems in modern finance can be cast into the framework of stochastic differential equations. The static 1D problem in financial engineering characterized by non-self-adjoint was examined in this paper by using the Quadra-ture Element Method （QEM）for the first time.The quadrature element for the problem mentioned above was established,and numerical results from QEM were compared with the analytic solution,FDM and FEM respectively.It is shown that high com-putational accuracy and efficiency are achieved using QEM,and this method can be further used in dynamic problem,2D prob-lem of financial engineering.