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We consider the problem of minimizing the shortfall risk when the aim is to hedge a contingent claim in a binomial market model and the initial capital is insufficient for a perfect hedge. This problem has been solved under complete information on the underlying model in [3]. We present two possible solutions to the same problem in the case of incomplete… (More)

The solution of a stochastic control problem depends on the underlying model. The actual real world model may not be known precisely and so one solves the problem for a hypothetical model, that is in general different but close to the real one; the optimal (or nearly optimal) control of the hypothetical model is then used as solution for the real problem.… (More)

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… (More)

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