  In this paper we consider the problem of calculating the quantiles of a risky
position, the dynamic of which is described as a continuous time
regime-switching jump-diffusion, by using Fourier Transform methods.
Furthermore, we study a classical option-based portfolio strategy which
minimizes the Value-at-Risk of the hedged position and show the impact of jumps
and switching regimes on the optimal strategy in a numerical example. However,
the analysis of this hedging strategy, as well as the computational technique
for its implementation, is fairly general, i.e. it can be applied to any
dynamical model for which Fourier transform methods are viable.
