Asset liquidity and the valuation of derivative securities

We consider the valuation of European-style derivative securities under limited asset liquidity through the dynamic management of a portfolio of assets effected through continuous transaction. The valuation arises from the optimal realization of a performance index relative to the set of all feasible portfolio trajectories. An approximation procedure based upon the method-of-lines finite element method is developed and analyzed; numerical examples are presented in order to demonstrate the viability of the approach.