Faculty of Mathematics, Physics and Informatics
STRIKE- Novel Methods in Computational Finance

Marie Curie International Training Network (ITN, 01/2013 - 12/2016)
This ITN Research Project STRIKE is supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE - Novel Methods in Computational Finance).

  Web page of the STRIKE ITN Network
at Bergische University of Wuppertal, Germany.
Comenius University Team leader   Team members
Prof. Daniel Sevcovic

Research interests
Computational finance
Partial differential equations
Geometric flows
Personal web page



Pedro Polvora
   Early Stage Research position

Dr. Silvie Kafková
   Experienced Researcher position
Dr. Sona Kilianova
   Dynamic stochastic programming, Stochastic simulations, Risk measures
Dr. Maria Trnovska
   Nonlinear programming, Convex optimization


Work package objectives   Publications of Bratislava STRIKE team members

The goal is to investigate qualitative and quantitative properties of solutions to nonlinear generalizations of the Black-Scholes (BS) equation. Nonlinear models can capture several important phenomena like transaction costs, investor's risk from unprotected portfolio, investor's expected utility maximization, illiquid markets, large traders feedback influence, etc.

  Such generalizations can be mathematically stated in the form of a nonlinear BS equation in which the volatility is adjusted to be a function of the Gamma of the option. Our approach is based on the analysis of the nonlinear BS equation for the Gamma of the option by means of combination of fully implicit and explicit finite difference methods (FDMs).

  Participating universities and intituitions



Associated Partners


  • Université Paris VI (Prof. Olivier Pironneau), Laboratoire Jacques-Louis Lions, U6 Paris, France.
  • University of Sussex (Dr. Bertram Düring), Department of Mathematics at University of Sussex, Brighton, UK.
  • University of A Coruña (Prof. Carlos Vázquez Cendón), M2NICA Research Group at Mathematics Department, University of A Coruña, Spain.
  • MathFinance AG (Prof. Uwe Wystup), Derivative Consulting, Waldems, Germany.
  • d-fine GmbH (Dr. Bodo Huckestein), Risk Modelling, Frankfurt am Main, Germany.
  • Postbank AG (Dr. Jörg Kienitz), Quantitative Analysis, Bonn, Germany.
  • Ortec Finance (Dr. Hens Steehouwer), Risk & Return Management, Rotterdam, the Netherlands.
  • ING Bank (Dr. Marc van Balen and Dr. Drona Kandhai), Corporate Market Risk Management, Amsterdam, the Netherlands.
  • Rabobank (Dr. Sacha van Weeren), Modelling & Research, Utrecht, the Netherlands.


Recent preprints

[5] K. Duris, Shih-Hau Tan, Choi-Hong Lai, and D. Sevcovic: Comparison of analytical approximation formula and New-ton’s method for solving a class of nonlinear Black-Scholes parabolic equations, to appear in: Computational Methods in Applied Mathematics

Published papers in reviewed scholarly journals


[4] S. Kilianova and M. Trnovska: Robust Portfolio Optimization via solution to the Hamilton-Jacobi-Bellman Equation, Int. Journal of Computer Mathematics, 2016.   DOI: 10.1080/00207160.2013.871542


[3] D. Sevcovic and M. Trnovska: Application of the Enhanced Semidefinite Relaxation Method to Construction of the Optimal Anisotropy Function, IAENG International Journal of Applied Mathematics, 45(3) (2015), 227-234

[2] D. Sevcovic and M. Trnovska: Solution to the Inverse Wulff Problem by Means of the Enhanced Semidefinite Relaxation Method,  Journal of Inverse and III-posed Problems, J. Inverse Ill-Posed Problems 23(3) 2015, 263-285

arXiv: 1402.5668     DOI:10.1515/jiip-2013-0069


[1] S. Kilianova and D. Sevcovic: A Transformation Method for Solving the Hamilton-Jacobi-Bellman Equation for a Constrained Dynamic Stochastic Optimal Allocation Problem, ANZIAM Journal (55) 2013, 14-38.
PDF file   Adobe     arXiv: 1307.3672     DOI: 10.1017/S144618111300031X

Papers in reviewed proceedings


Disclaimer: These papers are available for free download. Their content is identical with author's final versions submitted for publication. The Copyright of published versions has been transferred to publishers.

Daniel Sevcovic

Department of Applied Mathematics and Statistics
Faculty of Mathematics, Physics and Informatics
Comenius University
Mlynska dolina
842 48 Bratislava, Slovakia
Tel: + 421-2-602 95 660 Fax: + 421-2-654 25 882
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