  We extend the QLBS model by reformulating via considering a large trader
whose transactions leave a permanent impact on the evolution of the exchange
rate process and therefore affect the price of contingent claims on such
processes. Through a hypothetical limit order book we quantify the exchange
rate altered by such transactions. We therefore define the quoted exchange rate
process, for which we assume the existence of a postulated hedging strategy.
Given the quoted exchange rate and postulated hedging strategy, we find an
optimal hedging strategy through batch-mode reinforcement learning given the
trader alters the course of the exchange rate process. We assume that the
trader has its own concept of fair price and we define our problem as finding
the hedging strategy with much lower transaction costs yet delivering a price
that well converges to the fair price of the trader. We show our contribution
results in an optimal hedging strategy with much lower transaction costs and
convergence to the fair price is obtained assuming sensible parameters.
