In this paper we find sufficient conditions for the continuity of the  utility maximization problem from terminal wealth under convergence in distribution of the underlying processes. We provide several examples which illustrate that without these conditions, we cannot generally expect continuity to hold. Finally, we apply our continuity results to numerical computations of the shortfall risk in the Heston model  .
In this paper we find sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We provide several examples which illustrate that without these conditions, we cannot generally expect continuity to hold. Finally, we apply our results to the computation of the minimum shortfall in the Heston model by building an appropriate lattice approximation .
A
value of the
R
under
with respect to the
R
continuity results to numerical computations of the shortfall risk
results to the computation of the minimum shortfall
A
by building an appropriate lattice approximation