  We present here a regress later based Monte Carlo approach that uses neural
networks for pricing high-dimensional contingent claims. The choice of specific
architecture of the neural networks used in the proposed algorithm provides for
interpretability of the model, a feature that is often desirable in the
financial context. Specifically, the interpretation leads us to demonstrate
that any contingent claim -- possibly high dimensional and path-dependent --
under the Markovian and the no-arbitrage assumptions, can be semi-statically
hedged using a portfolio of short maturity options. We show how the method can
be used to obtain an upper and lower bound to the true price, where the lower
bound is obtained by following a sub-optimal policy, while the upper bound by
exploiting the dual formulation. Unlike other duality based upper bounds where
one typically has to resort to nested simulation for constructing
super-martingales, the martingales in the current approach come at no extra
cost, without the need for any sub-simulations. We demonstrate through
numerical examples the simplicity and efficiency of the method for both pricing
and semi-static hedging of path-dependent options

Computational Finance