Dimension-Wise Decompositions and Their Efficient Parallelization

Many problem classes in finance lead to high dimensional partial differential equations which need to be solved efficiently. To circumnavigate the curse of dimension several methods exist, e.g. dimension-wise decomposition techniques. In this chapter we will present an overview over the different methods available to cope with high dimensional problems. The class of dimension-wise decomposition methods, which we will discuss in detail, decomposes a high dimensional problem into a set of low dimensional problems. Dependent on the dimension d of the total problem, and the order of the decomposition method the number of low-dimensional problems can be quite large. This makes efficient parallelization techniques necessary