7,139 research outputs found

    Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements

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    This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundary conditions are illustrated for European vanilla options, digital call and American put options. The convection dominated Heston model for vanishing volatility is efficiently solved utilizing the adaptive dGFEM. For fast solution of the linear complementary problem of the American options, a projected successive over relaxation (PSOR) method is developed with the norm preconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option pricing by conducting comparison analysis with other methods and numerical experiments

    Sequential optimization for efficient high-quality object proposal generation

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    We are motivated by the need for a generic object proposal generation algorithm which achieves good balance between object detection recall, proposal localization quality and computational efficiency. We propose a novel object proposal algorithm, BING ++, which inherits the virtue of good computational efficiency of BING [1] but significantly improves its proposal localization quality. At high level we formulate the problem of object proposal generation from a novel probabilistic perspective, based on which our BING++ manages to improve the localization quality by employing edges and segments to estimate object boundaries and update the proposals sequentially. We propose learning the parameters efficiently by searching for approximate solutions in a quantized parameter space for complexity reduction. We demonstrate the generalization of BING++ with the same fixed parameters across different object classes and datasets. Empirically our BING++ can run at half speed of BING on CPU, but significantly improve the localization quality by 18.5 and 16.7 percent on both VOC2007 and Microhsoft COCO datasets, respectively. Compared with other state-of-the-art approaches, BING++ can achieve comparable performance, but run significantly faster

    Sequential Optimization for Efficient High-Quality Object Proposal Generation

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    We are motivated by the need for a generic object proposal generation algorithm which achieves good balance between object detection recall, proposal localization quality and computational efficiency. We propose a novel object proposal algorithm, BING++, which inherits the virtue of good computational efficiency of BING but significantly improves its proposal localization quality. At high level we formulate the problem of object proposal generation from a novel probabilistic perspective, based on which our BING++ manages to improve the localization quality by employing edges and segments to estimate object boundaries and update the proposals sequentially. We propose learning the parameters efficiently by searching for approximate solutions in a quantized parameter space for complexity reduction. We demonstrate the generalization of BING++ with the same fixed parameters across different object classes and datasets. Empirically our BING++ can run at half speed of BING on CPU, but significantly improve the localization quality by 18.5% and 16.7% on both VOC2007 and Microhsoft COCO datasets, respectively. Compared with other state-of-the-art approaches, BING++ can achieve comparable performance, but run significantly faster.Comment: Accepted by TPAM

    Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model

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    The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of Q by construction, it was only shown very recently that the spin representation can be promoted to the same level of generality. In this paper we show how to define the Potts model in terms of observables that simultaneously keep track of the spin and FK degrees of freedom. This is first done algebraically in terms of a transfer matrix that couples three different representations of a partition algebra. Using this, one can study correlation functions involving any given number of propagating spin clusters with prescribed colours, each of which contains any given number of distinct FK clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the Kac form h_{r,s}, with integer indices r,s that we determine exactly both in the bulk and in the boundary versions of the problem. In particular, we find that the set of points where an FK cluster touches the hull of its surrounding spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains this set to points where the neighbouring spin cluster extends to infinity, we show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table
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