A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementationComment: 25 page

A Unified Optimization Approach for Sparse Tensor Operations on GPUs

Sparse tensors appear in many large-scale applications with multidimensional and sparse data. While multidimensional sparse data often need to be processed on manycore processors, attempts to develop highly-optimized GPU-based implementations of sparse tensor operations are rare. The irregular computation patterns and sparsity structures as well as the large memory footprints of sparse tensor operations make such implementations challenging. We leverage the fact that sparse tensor operations share similar computation patterns to propose a unified tensor representation called F-COO. Combined with GPU-specific optimizations, F-COO provides highly-optimized implementations of sparse tensor computations on GPUs. The performance of the proposed unified approach is demonstrated for tensor-based kernels such as the Sparse Matricized Tensor- Times-Khatri-Rao Product (SpMTTKRP) and the Sparse Tensor- Times-Matrix Multiply (SpTTM) and is used in tensor decomposition algorithms. Compared to state-of-the-art work we improve the performance of SpTTM and SpMTTKRP up to 3.7 and 30.6 times respectively on NVIDIA Titan-X GPUs. We implement a CANDECOMP/PARAFAC (CP) decomposition and achieve up to 14.9 times speedup using the unified method over state-of-the-art libraries on NVIDIA Titan-X GPUs

A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementationbackward stochastic differential equations, parallel computing, Monte- Carlo methods, non linear PDE, American options, local volatility model.

A Study of Speed of the Boundary Element Method as applied to the Realtime Computational Simulation of Biological Organs

In this work, possibility of simulating biological organs in realtime using the Boundary Element Method (BEM) is investigated. Biological organs are assumed to follow linear elastostatic material behavior, and constant boundary element is the element type used. First, a Graphics Processing Unit (GPU) is used to speed up the BEM computations to achieve the realtime performance. Next, instead of the GPU, a computer cluster is used. Results indicate that BEM is fast enough to provide for realtime graphics if biological organs are assumed to follow linear elastostatic material behavior. Although the present work does not conduct any simulation using nonlinear material models, results from using the linear elastostatic material model imply that it would be difficult to obtain realtime performance if highly nonlinear material models that properly characterize biological organs are used. Although the use of BEM for the simulation of biological organs is not new, the results presented in the present study are not found elsewhere in the literature.Comment: preprint, draft, 2 tables, 47 references, 7 files, Codes that can solve three dimensional linear elastostatic problems using constant boundary elements (of triangular shape) while ignoring body forces are provided as supplementary files; codes are distributed under the MIT License in three versions: i) MATLAB version ii) Fortran 90 version (sequential code) iii) Fortran 90 version (parallel code

DWSI: AN APPROACH TO SOLVING THE POLYGON INTERSECTION-SPREADING PROBLEM WITH A PARALLEL UNION ALGORITHM AT THE FEATURE LAYER LEVEL

A dual-way seeds indexing (DWSI) method based on R-tree and the OpenGeospatial Consortium (OGC) simple feature model was proposed to solve the polygon intersection-spreading problem. The parallel polygon union algorithm based on the improved DWSI and the OpenMP parallel programming model was developed to validate the usability of the data partition method. The experimental results reveal that the improved DWSI method can implement a robust parallel task partition by overcoming the polygon intersection-spreading problem. The parallel union algorithm applied DWSI not only scaled up the data processing but alsospeeded up the computation compared with the serial proposal, and it showed ahigher computational efficiency with higher speedup benchmarks in the treatment of larger-scale dataset. Therefore, the improved DWSI can be a potential approach to parallelizing the vector data overlay algorithms based on the OGC simple data model at the feature layer level

DWSI: AN APPROACH TO SOLVING THE POLYGON INTERSECTION-SPREADING PROBLEM WITH A PARALLEL UNION ALGORITHM AT THE FEATURE LAYER LEVEL

A dual-way seeds indexing (DWSI) method based on R-tree and the OpenGeospatial Consortium (OGC) simple feature model was proposed to solve the polygon intersection-spreading problem. The parallel polygon union algorithm based on the improved DWSI and the OpenMP parallel programming model was developed to validate the usability of the data partition method. The experimental results reveal that the improved DWSI method can implement a robust parallel task partition by overcoming the polygon intersection-spreading problem. The parallel union algorithm applied DWSI not only scaled up the data processing but alsospeeded up the computation compared with the serial proposal, and it showed ahigher computational efficiency with higher speedup benchmarks in the treatment of larger-scale dataset. Therefore, the improved DWSI can be a potential approach to parallelizing the vector data overlay algorithms based on the OGC simple data model at the feature layer level