Research in the field of dynamic financial and portfolio management models is primarily focused on dynamic stochastic programming in order to maximize utility due to the dynamically changing weights of individual portfolio components. We use methods based on the solution of the Hamilton-Jacobi-Bellman partial differential equation and its suitable transformations. We propose efficient and stable numerical schemes for solving underlying equations. The results are applied mainly in the field of dynamic optimal management of retirement pension funds.
Brunovský, P., Černý, A., Komadel, J.: Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions, European Journal of Operational Research 264(3), 2018, pp. 1159-1171.
S. Kilianová, M. Trnovská: Robust Portfolio Optimization via Hamilton-Jacobi-Bellman Equation, International Journal of Computer Mathematics, Vol. 93, No. 5, 2016, 725-734.
S. Kilianová and D. Ševčovič: A Transformation Method for Solving the Hamilton-Jacobi-Bellman Equation for a Constrained Dynamic Stochastic Optimal Allocation Problem, ANZIAM Journal (55) 2013, 14-38.
N. Ishimura, D. Ševčovič: On traveling wave solutions to a Hamilton-Jacobi-Bellman equation with inequality constraints, Japan Journal of Industrial and Applied Mathematics 30(1) 2013, 51-67.
I. Melicherčík and D. Ševčovič: Dynamic Stochastic Accumulation Model with Application to Pension Savings Management, Yugoslav Journal of Operations Research, 2010 20(1):1-24.
T. Jakubik, I. Melicherčík, D. Ševčovič: Sensitivity analysis for a dynamic stochastic accumulation model for optimal pension savings management, Ekonomický časopis, 8, 2009, 756-771.