  A trading system is said to be {robust} if it generates a robust return
regardless of market direction. To this end, a consistently positive expected
trading gain is often used as a robustness metric for a trading system. In this
paper, we propose a new class of trading policies called the {double linear
policy} in an asset trading scenario when the transaction costs are involved.
Unlike many existing papers, we first show that the desired robust positive
expected gain may disappear when transaction costs are involved. Then we
quantify under what conditions the desired positivity can still be preserved.
In addition, we conduct heavy Monte-Carlo simulations for an underlying asset
whose prices are governed by a geometric Brownian motion with jumps to validate
our theory. A more realistic backtesting example involving historical data for
cryptocurrency Bitcoin-USD is also studied.
