Názov:
A Method of Solving Hamilton-Jacobi-Bellman Equation for Constrained
Optimal Investment Problem via Riccati Transformation

Abstrakt:
In this talk we propose and analyze a method based on the Riccati
transformation for solving the Hamilton-Jacobi-Bellman equation. Such an
equation typically arises in modeling of optimal portfolio investment on
a finite time horizon, subject to range constraints on portfolio
composition. Its solution can be interpreted as the optimal feedback
strategy for a stochastic dynamic optimization problem of a multi-asset
portfolio allocation. 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 solutions. We compute optimal strategies for
a portfolio investment problem motivated by the fully funded pension
saving system in Slovakia and by the German DAX 30 Index as examples of
application of the method.