Optimal portfolio allocation with volatility and co-jump risk that Markowitz would like

We study a continuous time optimal portfolio allocation problem with volatility and co-jump risk, allowing prices, variances and covariances to jump simultaneously. Differently from the traditional approach, we deviate from... [ view full abstract ]

We study a continuous time optimal portfolio allocation problem with volatility and co-jump risk, allowing prices, variances and covariances to jump simultaneously. Differently from the traditional approach, we deviate from affine models by specifying a flexible Wishart jump-diffusion for co-precision (inverse of covariance matrix). The optimal portfolio weights which solve the dynamic programming problem are genuinely dynamic and proportional to the instantaneous co-precision, reconciling optimal dynamic allocation with the static Markowitz-type economic intuition. Numerical experiments show the accuracy of the proposed approximation and quantify the effect, based on a calibration on historical U.S. data, of price/volatility co-jumps on portfolio selection