F. Herzog, H.P. Geering, and L.M. Schumann (Switzerland)
Portfolio management, risk analysis, optimization, stochas tic control, time series analysis
This paper develops a discrete-time portfolio optimization for multi asset and long term investment objective. The expected returns of the risky assets are modelled using a factor model based on linear stochastic processes. A multivariable Generalized Autoregressive Conditional Het eroskedasticity (GARCH) model describes volatilities and correlations of the risky assets. The portfolio optimization is solved with respect to a coherent risk measure over ter minal wealth steps into the future. As a suitable risk mea sure we use Conditional Value-at-Risk, since it is coherent and computationally efficient. In order to solve this time varying portfolio management problem, a dynamic opti mization approach is proposed to obtain the decision rules for the optimal portfolio allocation. The portfolio optimiza tion is based on a large-scale Monte-Carlo simulation and linear programming.
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