An optimal execution problem with market impact
The paper deals with the optimal execution problem when an impact of a continuous-time market model is considered. The problem is formulated as a stochastic control problem where properties of the corresponding value function are investigated. First one studies the continuity of the value function: the obtained results e.g. show that an instantaneous liquidation of large volume makes no sense when the market impact for large trade is strong. Further one shows the validity of Bellman principle (i.e. the semigroup property) so that the value function can be characterised as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. Finally, a case is considered where the trader needs to liquidate all holdings of the security: it is shown that such a liquidation does not influence the form of the corresponding value function.
scientific article; zbMATH DE number 6348477
scientific article