A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation

We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we show that a piecewise-constant dual control provides a good approximation on a short interval. A dynamic programming algorithm extends the approximation to a finite time horizon. Finally, we illustrate the application of the procedure to financial risk management in conjunction with nested simulation and on an multidimensional portfolio valuation problem

Optimizing the MapReduce Framework on Intel Xeon Phi Coprocessor

With the ease-of-programming, flexibility and yet efficiency, MapReduce has become one of the most popular frameworks for building big-data applications. MapReduce was originally designed for distributed-computing, and has been extended to various architectures, e,g, multi-core CPUs, GPUs and FPGAs. In this work, we focus on optimizing the MapReduce framework on Xeon Phi, which is the latest product released by Intel based on the Many Integrated Core Architecture. To the best of our knowledge, this is the first work to optimize the MapReduce framework on the Xeon Phi. In our work, we utilize advanced features of the Xeon Phi to achieve high performance. In order to take advantage of the SIMD vector processing units, we propose a vectorization friendly technique for the map phase to assist the auto-vectorization as well as develop SIMD hash computation algorithms. Furthermore, we utilize MIMD hyper-threading to pipeline the map and reduce to improve the resource utilization. We also eliminate multiple local arrays but use low cost atomic operations on the global array for some applications, which can improve the thread scalability and data locality due to the coherent L2 caches. Finally, for a given application, our framework can either automatically detect suitable techniques to apply or provide guideline for users at compilation time. We conduct comprehensive experiments to benchmark the Xeon Phi and compare our optimized MapReduce framework with a state-of-the-art multi-core based MapReduce framework (Phoenix++). By evaluating six real-world applications, the experimental results show that our optimized framework is 1.2X to 38X faster than Phoenix++ for various applications on the Xeon Phi

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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