Seminár z kvalitatívnej teórie diferenciálnych rovníc

Štvrtok 22.11.2012 o 13:30 v miestnosti M-223

Daniel Ševčovič (KMAŠ FMFI UK): A method of solving Hamilton-Jacobi-Bellman equation with constraints via Riccati transformation

Abstrakt:

In this talk we propose and analyze a method based on the Riccati transformation for solving Hamilton-Jacobi-Bellman equation, arising from a problem of optimal portfolio construction. We show how the fully nonlinear Hamilton-Jacobi-Bellman equation can be transformed into a quasi-linear parabolic equation for which we prove existence, uniqueness and derive useful bounds of classical Holder smooth solutions. We furthermore construct a fully implicit iterative numerical scheme based on finite volume approximation of the governing equation. A numerical solution is compared to a semi-explicit traveling wave solution by means of the convergence ratio of the method. We compute optimal strategies for a portfolio investment problem with state constraints.

This is joint work with Soňa Kilianová.