Shortfall risk minimising strategies in the binomial model: characterisation and convergence

In this paper we study the dependence on the loss function of the strategy, which minimises the expected shortfall risk when dealing with a financial contingent claim in the particular situation of a binomial model. After having characterised the optimal strategies in the particular cases when the loss function is concave, linear or strictly convex, we analyse how optimal strategies change when we approximate a loss function with a sequence of suitable loss functions. The particular case of lower partial moments is considered as an example.