Dispensing with optimal control: a new approach for the pricing and management of share buyback contracts

Abstract

This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state spaces and the intricacies of selecting appropriate risk penalty or risk aversion parameter. Our methodology applies optimized heuristic strategies to maximize the contract's value. The computation of this value utilizes classical methods typically used for pricing path-dependent options. Additionally, our approach naturally leads to the formulation of a $Δ$-hedging strategy and disentangles therefore the repurchase strategy from the hedging of the payoff.