We analyze the consumption-portfolio selection problem of an investor facing both Brownian and jump risks. We bring new tools, in the form of orthogonal decompositions, to bear on the problem in order to determine the optimal portfolio in closed form. We show that the optimal policy is for the investor to focus on controlling his exposure to the jump risk, while exploiting differences in the Brownian risk of the asset returns that lies in the orthogonal space.
"Portfolio choice with jumps: A closed-form solution." Ann. Appl. Probab. 19 (2) 556 - 584, April 2009. https://doi.org/10.1214/08-AAP552