Optimal hedging when the underlying asset follows a regime-switching Markov process

•A flexible discrete-time hedging approach for a general regime-switching framework.•Minimization of the expected value of any desired penalty function of the hedging error.•Backward recursion allows for the sequential construction of an optimal strategy.•Efficient numerical implementation is described.

We develop a flexible discrete-time hedging methodology that minimizes the expected value of any desired penalty function of the hedging error within a general regime-switching framework. A numerical algorithm based on backward recursion allows for the sequential construction of an optimal hedging strategy. Numerical experiments comparing this and other methodologies show a relative expected penalty reduction ranging between 0.9%0.9% and 12.6%12.6% with respect to the best benchmark.