查看更多>>摘要：This paper focuses on the pricing of continuous geometric Asian options (GAOs) under a new multifactor stochastic volatility model. The model considers fast and slow mean reverting factors of volatility, where slow volatility factor is approximated by a quadratic arc. The asymptotic expansion of the price function is assumed, and the first order price approximation is derived using the perturbation techniques for both floating and fixed strike GAOs. Much simplified pricing formulae for the GAOs are obtained in this multifactor stochastic volatility framework. The zeroth order term in the price approximation is the modified Black-Scholes price for the GAOs. This modified price is expressed in terms of the Black-Scholes price for the GAOs. The accuracy of the approximate option pricing formulae is established, and also verified numerically by comparing the model prices with the Monte Carlo simulation prices and the Black- Scholes prices for the GAOs. The model parameter is estimated by capturing the volatility smiles. The sensitivity analysis is also performed to investigate the effect of underlying parameters on the approximated prices. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua and capturing non-local transfer and effective properties in the computational domain via constructing localized multiscale basis functions. The construction of the basis functions consists of solving local problems defined on oversampling computational region, subject to the energy minimizing constraints that the mean values of the local solution are zero in all continua except for the one targeted. The basis functions constructed are shown to have good approximation properties. It is shown that the method has a coarse mesh dependent convergence. We present some numerical examples to illustrate the performance of the proposed method. (c) 2021 Published by Elsevier B.V.
查看更多>>摘要：A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial splines, the related parametric curves exhibit the desired properties of convex hull inclusion, variation diminution and intuitive relation between the curve shape and the location of the control points. For a good-for-design space, in this paper we construct a set of functions, called transition functions, which allow for efficient computation of the B-spline basis, even in the case of nonuniform and multiple knots. Moreover, we show how the spline coefficients of the representations associated with a refined knot partition and with a raised order can conveniently be expressed by means of transition functions. This result allows us to provide effective procedures that generalize the classical knot insertion and degree raising algorithms for polynomial splines. We further discuss how the approach can straightforwardly be generalized to deal with geometrically continuous piecewise Chebyshevian splines as well as with splines having section spaces of different dimensions. From a numerical point of view, we show that the proposed evaluation method is easier to implement and has higher accuracy than other existing algorithms. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A modified weak Galerkin finite element method is studied for nonmonotone quasilinear elliptic problems. Using the contraction mapping theorem, the uniqueness of the solution to the discrete problem is proved. Moreover, optimal order a priori error estimates are established in both a discrete H-1 norm and the L-2 norm. Numerical experiments are conducted to confirm the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We analytically and numerically solve the PCP equation, u(xx)u(yy) = 1, with homogeneous Dirichlet boundary conditions on the unit square. Chebyshev and Fourier spectral methods with low degree truncations yield moderate accuracy but the usual exponential rate of convergence of spectral methods is destroyed by the boundary singularities of the solution. In the sequel to this work, we will apply a variety of strategies including a change-of-coordinates and singular basis functions to recover spectral accuracy in spite of the boundary singularities. As preparation for this numerical study, we find explicit solutions to related problems to the two-dimensional PCP equation in a domain with a boundary that is an ellipse and the three-dimensional PCP equation in a cubic domain. We also analyze the boundary behavior of these solutions: all have complicated singularities with unbounded first derivatives. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Starting from the matrix form of the fractional Cauchy problem, new formulae for the sum of the three-parameter Mittag-Leffler functions are deduced. The derivation is based on the Prabhakar fractional integral operator. A Volterra integral equation relating the solution of the Cauchy problem with that of a perturbed problem is also obtained; from this a condition number measuring the sensitivity of the solution to changes in data can be derived. Several examples are also incorporated to test the bounds. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Starting with the simplest case of an analogue square root control-system, we extend the idea to the discrete-time case and ultimately the multivariable discrete-time case. Several new results then emerge from the multivariable work. A nonlinear system is designed to take the square root of an arbitrary square matrix. The matrix can have real or complex values and an analysis of stability is reached by using matrix calculus and nonlinear theory. The root-locus of the multivariable system exhibits straight-line characteristics which has not been observed before and to achieve stability we introduce the concept of a complex step-size (or gain) in a recursive square root algorithm. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We show that the LSPIA method for curve and surface approximation, which was introduced by Deng and Lin (2014), is equivalent to a gradient descent method. We also note that Deng and Lin's results concerning feasible values of the stepsize are directly implied by classical results about convergence properties of the gradient descent method. We propose a modification based on stochastic gradient descent, which lends itself to a realization that employs the technology of neural networks. In addition, we show how to incorporate the optimization of the parameterization of the given data into this framework via parameter correction (PC). This leads to the new LSPIA-PC method and its neural-network based implementation. Numerical experiments indicate that it gives better results than LSPIA with comparable computational costs. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there are efficient algorithms for determining such adaptive splines, the difficulty with TV regularization is that the solution is generally non-unique, an aspect that is often ignored in practice. In this paper, we present a systematic analysis that results in a complete description of the solution set with a clear distinction between the cases where the solution is unique and those, much more frequent, where it is not. For the latter scenario, we identify the sparsest solutions, i.e., those with the minimum number of knots, and we derive a formula to compute the minimum number of knots based solely on the data points. To achieve this, we first consider the problem of exact interpolation which leads to an easier theoretical analysis. Next, we relax the exact interpolation requirement to a regression setting, and we consider a penalized optimization problem with a strictly convex data-fidelity cost function. We show that the underlying penalized problem can be reformulated as a constrained problem, and thus that all our previous results still apply. Based on our theoretical analysis, we propose a simple and fast two-step algorithm, agnostic to uniqueness, to reach a sparsest solution of this penalized problem. (C)& nbsp;2021 The Author(s). Published by Elsevier B.V.& nbsp;
查看更多>>摘要：Two fast numerical algorithms are proposed for computing interval vectors containing positive solutions to M-tensor multi-linear systems. The first algorithm involves only two tensor-vector multiplications. The second algorithm is iterative one, and generally gives interval vectors narrower than those by the first algorithm. We also develop two verification algorithms for Perron vectors of a kind of weakly irreducible nonnegative tensors, which we call slightly positive tensors. The first and second algorithms have properties similar to those of the two algorithms for the solutions to the M-tensor systems. We clarify relations between slightly positive tensors and other tensor classes. Numerical results show efficiency of the algorithms. (C) 2021 Elsevier B.V. All rights reserved.
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