Monte Carlo scalable algorithms for Computational Finance

With the latest developments in the area of advanced computer architectures, we are already seeing large scale machines at petascale level and we are faced with the exascale computing challenge. All these require scalability at system, algorithmic and mathematical model level. In particular, e_cient scalable algorithms are required to bridge the performance gap. In this paper, examples of various approaches of designing scalable algorithms for such advanced architectures will be given. We will briefly present our approach to Monte Carlo scalable algorithms for Linear Algebra and explain how these approaches are extended to the field of Computational Finance. Implementation examples will be presented using Linear Algebra Problems and problems from Computational Finance. Furthermore, the corresponding properties of these algorithms will be outlined and discussed