Optimal Impulse Control of Portfolios

An investor has the opportunity of holding shares in n risky assets and one nonrisky asset at every time in a fixed interval [t, T]. The risky assets are governed by a stochastic differential equation. At random instants of his choice he may intervene in order to rebalance his portfolio and consume a nonnegative amount of money. Fixed and variable transactions costs are incurred upon intervention. At time T all remaining wealth is consumed. The solution to the problem of maximizing total utility of consumption is given by way of quasi-variational inequalities for the value function. With probability one the investor only intervenes finitely many times. Indication of the solution of the quasi-variational inequalities in the case of one risky asset with log-normal prices is given, together with a description of a discretization procedure.