BFS 2002

Poster Presentation

We consider the problem of shortfall risk minimisation in the binomial model when the loss function is not specified, and analyse the robustness of shortfall risk minimising strategy with respect to the loss function. We find closed form solutions for the cases of convex and concave loss functions both for the strategy as for the expected shortfall. We also find out that in the particular case of minimising lower partial moments of order $\kappa$ of the final wealth, the optimal strategies are continuous with respect to $\kappa$ for $\kappa \geq 1$, and there can be a discontinuity for $\kappa < 1$.