Daniel Sevcovic

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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)
We propose a direct method for solving the evolution of plane curves satisfying the geometric equation Ú ¬´ÜÜ µ where Ú is the normal velocity, and are the curvature and tangential angle of a plane curve Ê ¾ at a point Ü ¾. We derive and analyze the governing system of partial differential equations for the curvature, tangential angle, local length and(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 ⊂ R 2 at a point x ∈ Γ. We derive and analyze the governing system of partial differential equations for the curvature, tangential angle, local(More)
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 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)
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 a linear(More)
It is well known [11] that the early exercise boundary for the American put approaches the strike price at expiry with infinite velocity. This causes difficulties in developing efficient and accurate numerical procedures and consequently trading strategies, during the volatile period near expiry. Based on the work of D. ˇ Sevčovič [10] for the Amer-ican(More)
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)
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)