金融与管理中的HJB方程组的高效有限元方法

By virtue of optimal partition and interpolation, integral identities, and interpolation postprocessing technique, we probe superconvergence, Richardson extrapolation, iterated and interpolation defect correction of finite element methods for the system of Hamilton-Jacobi-Bellman partial differential equations in finance and management. In addition, on the basis of these finite element methods of higher efficiency, some reliable a posteriori error estimators are provided, and thus adaptive and parallel algorithms can be constructed, which can develop and enrich the theories and applications of the finite element methods of higher efficiency. This provides scientifc foundation for solving the valuation of financial derivatives and the governing of haza, and improves the mathematical level of solving similar real problems.

利用最优剖分与最优插值、积分恒等式与插值后处理等超逼近分析技术，研究金融与管理中Hamilton-Jacobi-Bellman偏微分方程组的有限元超收敛、Richardson外推、迭代与插值校正等高效算法，并籍此构造出相应算法的可靠的后验误差指示子，进而建立高效有限元的自适应算法与并行算法，发展和丰富高效自适应与并行有限元方法的理论与应用，为金融衍生品定价与雾霾治理等问题的解决提供基础科学支撑，提高这类实际问题研究的数学水平。

利用最优剖分与最优插值、积分恒等式与插值后处理等超逼近分析技术，研究金融与管理中Hamilton-Jacobi-Bellman偏微分方程组的有限元超收敛、Richardson外推、迭代与插值校正等高效算法，并籍此构造出相应算法的可靠的后验误差指示子，进而建立高效有限元的自适应算法与并行算法，发展和丰富高效自适应与并行有限元方法的理论与应用，为金融衍生品定价与雾霾治理等问题的解决提供基础科学支撑，提高这类实际问题研究的数学水平。