Graduate Student Seminars
نویسندگان
چکیده
We develop the optimal trading strategy for our broker who has non-zero inventory in three currency pairs with different level of liquidity and would like to o ff-load all inventories with a given time schedule while accepting exogenous clients orders. The mid-exchange rate satisfies constraint to exclude the triangle arbitrage. Our broker is risk-neutral, inventory averse and would like to maximize the overall trading wealth denominated in her local currency. Unlike the case of liquidating individual asset separately, the appropriate form of inventory penalty should be consisted by both the square of individual inventory and their cross product. We propose an appropriate form of running inventory penalty by imposing ambiguity aversion on the drifts of mid-exchange rates. In our model, we can find the closed form solution for the value function and an optimal Markovian control of the stochastic control problem. Verification proofs are provided.
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