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

The QLBS Model within the presence of feedback loops through the impacts of a large trader