Before revision: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts. In addition, it is supposed that the market participants can partially infer the position size held by the market maker and their aggregate reactions affect the security prices. Although the market maker can ask its OTC counterparties to transact a block trade without causing a direct price impact in the exchange, its timing is assumed to be uncertain.
After revision: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC counterparties to transact a block trade without causing a direct price impact in the exchange, its timing is assumed to be uncertain.