Impulse control of portfolios with jumps and transaction costs

Abstract

An investor holds shares in one risky asset and one non-risky asset for a finite time period. The risky asset moves according to a geometric Brownian motion with jumps at the times of a Poisson process. The investor is to choose instants at which to rebalance the portfolio, pay fixed and variable transaction costs, and consume a non-negative amount of wealth. Total expected discounted consumption is to be maximized. The optimal investment plan is characterized in terms of quasi-variational inequalities. Properties of the optimal solution are derived without recourse to numerical computation.

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