Exact Optimization of Path-Dependent Performance Measures for Single Asset Trading with Side Information
This thesis develops an efficient training method for optimizing path-dependent
performance measures in single asset trading scenarios using gradient descent.
We compute the exact, path-dependent gradients for both linear and nonlinear
decision models. We account for transaction costs as a fixed percentage
of any trading decision relative to the magnitude of the size in position
change. We apply our method to two measures of performance for price series of
T steps: mean return and the Sharpe ratio. For linear models, we achieve a
training complexity of O(TL) where L represents a fixed number of previous
time steps considered for the current decision. Neural networks with a single
hidden layer require O(TH^2L) to train for a hidden layer of size H. We
allow long positions, short positions, and decisions can scale to arbitrary
ranges to better fit real world scenarios like margin buying. Experimental
results on both synthetic and real-world price series demonstrate both correct
learning and the ability to capture and take advantage of mispricing in the
market via techniques like pairs trading.