We consider a market consisting of one safe and one risky asset, which offer constant investment opportunities. Taking into account both proportional transaction costs and linear price impact, we derive optimal rebalancing policies for representative investors with constant relative risk...

Abstract For any utility function with asymptotic elasticity equal to one, we construct a market model in countable discrete time, such that the utility maximization problem with proportional transaction costs admits no solution. This proves that the necessity of the reasonable asymptotic...