Optimal Portfolios when Variances and Covariances can Jump

We analyze the optimal portfolio choice in a multi-asset Wishart-model in which return variances and correlations are stochastic and subject to jump risk. The optimal portfolio is characterized by the positions in stock diffusion risk, variance-covariance diffusion risk, and jump risk. We find that including jumps in the second moments changes the optimal positions and particularly variance-covariance hedging demands significantly. Furthermore, we show that the utility gains from market completeness are significant. They increase in the amount of uncertainty in second moments, in particular in the size of variance-covariance jumps and in the intensity of jumps. As a robustness check, we compare our results to those obtained for other parametrizations of Wishart-models from the literature as well as to various single-asset models