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Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization

Soňa Kilianová, Daniel Ševčovič (2018)

Kybernetika

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ( C V a R D ) based Sharpe ratio for measuring...

Exponential decay of a solution for some parabolic equation involving a time nonlocal term

Kota Kumazaki (2015)

Mathematica Bohemica

We consider the large time behavior of a solution of a parabolic type equation involving a nonlocal term depending on the unknown function. This equation is proposed as a mathematical model of carbon dioxide transport in concrete carbonation process, and we proved the existence, uniqueness and large time behavior of a solution of this model. In this paper, we derive the exponential decay estimate of the solution of this model under restricted boundary data and initial data.

Finite difference scheme for the Willmore flow of graphs

Tomáš Oberhuber (2007)

Kybernetika

In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in Oberhuber [Obe-2005-2,Obe-2005-1] which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry of the solution. Since it requires higher regularity of the solution, additional...

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