Consumption-investment optimization problem in a Lévy financial model with transaction costs and làdlàg strategies

We consider the consumption-investment optimization problem for the financial market model with constant proportional transaction rates and Levy price process dynamics. Contrarily to the recent work of De Valliere (Financ Stoch 20:705–740, 2016), portfolio process trajectories are only left and right limited. This allows us to identify an optimal ladlag strategy, e.g. in the two dimensional case, as it is possible to suitably rebalance the portfolio processes when they jump out of the no-trade region in the solvency cone.