  In this article, we introduce an algorithm called Backward Hedging, designed
for hedging European and American options while considering transaction costs.
The optimal strategy is determined by minimizing an appropriate loss function,
which is based on either a risk measure or the mean squared error of the
hedging strategy at maturity. The proposed algorithm moves backward in time,
determining, for each time-step and different market states, the optimal
hedging strategy that minimizes the loss function at the time the option is
exercised, by assuming that the strategy used in the future for hedging the
liability is the one determined at the previous steps of the algorithm. The
approach avoids machine learning and instead relies on classic optimization
techniques, Monte Carlo simulations, and interpolations on a grid. Comparisons
with the Deep Hedging algorithm in various numerical experiments showcase the
efficiency and accuracy of the proposed method.
