Dynamic portfolio allocation in complete markets with co-jumps

In this paper, we solve a continuous-time dynamic optimal portfolio allocation problem in a complete market setup, by considering non-affine dynamics for the state variables, since we model precision instead of volatility, intended as the reciprocal of volatility, where both the stock and variance processes are subject to discontinuities. Such non-affine framework ensures a closed-form expression for the optimal weights of all the financial assets involved, namely a riskless security, an equity and traded derivatives on such equity. The solution to the optimal allocation is genuinely dynamic, consistently with the well-known Markowitz economic intuition that an inverse dependence of the portfolio exposures with respect to the variability parameters should be observed. In order to uncover the role of jumps in the optimal allocation, we numerically investigate some instances of the non-affine model proposed and analyze the corresponding risk profile. Furthermore, we perform a calibration procedure on real data, revealing that the performances of our investment strategy greatly benefits from the presence of both derivatives and co-jumps.