Impulsive control of portfolios

In the paper a general model of a market with asset prices and economical factors of Markovian structure is considered. The problem is to find optimal portfolio strategies maximizing a discounted infinite horizon reward functional consisting of an integral term measuring quality of the portfolio at each moment and a discrete term measuring the reward from consumption. There are general transaction costs which, in particular, cover fixed plus proportional costs. It is shown, under general conditions, that there exists an optimal impulse strategy and the value function is a solution to the Bellman equation which corresponds to suitable quasi-variational inequalities.