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We analyse a model for pricing derivative securities in the presence of both transaction costs as well as the risk from a volatile portfolio. The model is based on the Black-Scholes parabolic PDE in which transaction costs are described following the Hoggard, Whalley, and Wilmott approach. The risk from a volatile portfolio is described by the variance of… (More)

We propose a direct method for solving the evolution of plane curves satisfying the geometric equation v= β(x, k, ν) where v is the normal velocity, k and ν are the curvature and tangential angle of a plane curve Γ ⊂ R2 at a point x ∈ Γ . We derive and analyze the governing system of partial differential equations for the curvature, tangential angle, local… (More)

- Daniel Sevcovic, Karol Mikula
- SIAM Journal of Applied Mathematics
- 2001

We study the intrinsic heat equation governing the motion of plane curves. The normal velocity v of the motion is assumed to be a nonlinear function of the curvature and tangential angle of a plane curve Γ. By contrast to the usual approach, the intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional α. Short… (More)

- Daniel Sevcovic
- 2008

Abstract. The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of generalized Black-Scholes equations. We analyze qualitatively and quantitatively the early exercise boundary for… (More)

We suggest a stable Lagrangian method for computing elastic curve evolution driven by the intrinsic Laplacian of curvature (called also surface diffusion of curves). The algorithm for solving such a geometric evolution is based on a numerical solution to a fourth order intrinsic diffusion equation. The stability of the method is enhanced on by… (More)

In this paper we investigate a two-phase minmax optimization method for parameter estimation of the well known Cox, Ingersoll, and Ross one-factor interest rate model (CIR). In the first optimization phase we determine four CIR parameters by minimizing the sum of squares of differences of a theoretical CIR yield curve and real market yield curve data. We… (More)

- Daniel Sevcovic
- 2008

The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black–Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A motivation for studying the nonlinear Black–Scholes equation with a nonlinear volatility arises from option pricing models… (More)

Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic e-mail: benes@kmlinux.fjfi.cvut.cz, e-mail: oberhuber@kmlinux.fjfi.cvut.cz Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovak Republic e-mail:… (More)

The evolution of plane curves obeying the equation v = β(k), where v is normal velocity and k curvature of the curve is studied. Morphological image and shape multiscale analysis of Alvarez, Guichard, Lions and Morel and affine invariant scale space of curves introduced by Sapiro and Tannenbaum as well as isotropic motions of plane phase interfaces studied… (More)

- Karol Mikula, Mariana Remesíková, Peter Sarkoci, Daniel Sevcovic
- SIAM J. Scientific Computing
- 2014

In this paper we propose several techniques for tangential redistribution of points on evolving surfaces. This is an important issue in numerical approximation of any Lagrangian evolution model, since the quality of the mesh has a significant impact on the result of the computation. We explain the volume-oriented and length-oriented tangential… (More)