Portfolio valuation under liquidity constraints with permanent price impact

When institutional investors rearrange their portfolios, they should consider both the temporary and the permanent price impacts. After a temporary price impact the order book fully recovers, whereas a permanent price impact changes the equilibrium price, having effects on the resulting portfolio. In this paper, for a given period, we introduce an optimization problem for valuing illiquid portfolios with permanent price impacts. We show how to find the optimal trade to satisfy certain portfolio constraints. As a policy implication, we note that introducing permanent price impacts in internal or external regulation can substantially change liquidity risk or capital requirements.