Prof. Dr. Rudi Zagst & Prof. Dr. Marcos Escobar-Anel
Abstract: This thesis solves a multi-period portfolio optimization problem for the Heston-Nandi GARCH (HN-GARCH) model and an investor maximizing utility from terminal wealth. Assuming a power utility function we produce closed formulas for the optimal investment strategy, the value function and the optimal wealth process for two different approximations of the self-financing condition (SFC). For one of the approximations the formulas have a recursive representation for the other one they have non-recursive representations. We find that the optimal investment strategy is independent of the development
of the risky asset, and that the solution under one of the SFC's converges to that of a continuous-time Heston stochastic volatility model (see [Kra05]), albeit under some additional conditions. Further, our strategy contains that of a geometric Brownian motion (GBM) from [Mer69] as a special case. For a daily trading scenario, the optimal solutions are quite robust to variations in the parameters, while a numerical wealth equivalent loss (WEL) analysis shows good performance of the Heston solution, with a quite inferior performance of the Merton solution.
Prof. Dr. Marcos Escobar-Anel, Prof. Dr. Rudi Zagst