Search results for "Meri"
showing 10 items of 7596 documents
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed
Iterative Methods for Pricing American Options under the Bates Model
2013
We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…
IMEX schemes for pricing options under jump–diffusion models
2014
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump-diffusion process. The schemes include the families of IMEX-midpoint, IMEX-CNAB and IMEX-BDF2 schemes. Each family is defined by a convex combination parameter [email protected]?[0,1], which divides the zeroth-order term due to the jumps between the implicit and explicit parts in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restric…
LOCAL CONTROL OF SOUND IN STOCHASTIC DOMAINS BASED ON FINITE ELEMENT MODELS
2011
A numerical method for optimizing the local control of sound in a stochastic domain is developed. A three-dimensional enclosed acoustic space, for example, a cabin with acoustic actuators in given locations is modeled using the finite element method in the frequency domain. The optimal local noise control signals minimizing the least square of the pressure field in the silent region are given by the solution of a quadratic optimization problem. The developed method computes a robust local noise control in the presence of randomly varying parameters such as variations in the acoustic space. Numerical examples consider the noise experienced by a vehicle driver with a varying posture. In a mod…
Higher-order Nonnegative CANDECOMP/PARAFAC Tensor Decomposition Using Proximal Algorithm
2019
Tensor decomposition is a powerful tool for analyzing multiway data. Nowadays, with the fast development of multisensor technology, more and more data appear in higherorder (order > 4) and nonnegative form. However, the decomposition of higher-order nonnegative tensor suffers from poor convergence and low speed. In this study, we propose a new nonnegative CANDECOM/PARAFAC (NCP) model using proximal algorithm. The block principal pivoting method in alternating nonnegative least squares (ANLS) framework is employed to minimize the objective function. Our method can guarantee the convergence and accelerate the computation. The results of experiments on both synthetic and real data demonstrate …
Force Distribution Analysis of Mechanochemically Reactive Dimethylcyclobutene
2013
Internal molecular forces can guide chemical reactions, yet are not straightforwardly accessible within a quantum mechanical description of the reacting molecules. Here, we present a force-matching force distribution analysis (FM-FDA) to analyze internal forces in molecules. We simulated the ring opening of trans-3,4-dimethylcyclobutene (tDCB) with on-the-fly semiempirical molecular dynamics. The self-consistent density functional tight binding (SCC-DFTB) method accurately described the force-dependent ring-opening kinetics of tDCB, showing quantitative agreement with both experimental and computational data at higher levels. Mechanical force was applied in two different ways, namely, exter…
Synchronization of hidden chaotic attractors on the example of radiophysical oscillators
2017
In the present paper we consider the problem of synchronization of hidden and self-excited attractors in the context of application to a system of secure communication. The system of two coupled Chua models was studied. Complete synchronization was observed as for self-excited, as hidden attractors. Beside it for hidden attractors some special type of dynamic was revealed.
Visualising maritime vessel open data for better situational awareness in ice conditions
2018
Situational awareness of maritime vessels in ice conditions is important for the operation of supply chains. In the artic sea areas, the ice conditions pose a major challenge for maritime vessels getting stuck in the ice and being significantly delayed in arrival to harbor. Data science and open data provide new opportunities to overcome these challenges. This paper introduces available open data sources and data visualizations that can be used to develop applications, for example, for detecting maritime vessel collision, predicting estimated time of arrival to harbor, as well as maritime vessel route optimization in ice conditions. The paper begins by introducing available open data source…