  When firms want to buy back their own shares, they have a choice between
several alternatives. If they often carry out open market repurchase, they also
increasingly rely on banks through complex buyback contracts involving option
components, e.g. accelerated share repurchase contracts, VWAP-minus
profit-sharing contracts, etc. The entanglement between the execution problem
and the option hedging problem makes the management of these contracts a
difficult task that should not boil down to simple Greek-based risk hedging,
contrary to what happens with classical books of options. In this paper, we
propose a machine learning method to optimally manage several types of buyback
contract. In particular, we recover strategies similar to those obtained in the
literature with partial differential equation and recombinant tree methods and
show that our new method, which does not suffer from the curse of
dimensionality, enables to address types of contract that could not be
addressed with grid or tree methods.
