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.
In this paper we find tight 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 also establish a weak convergence result for the terminal wealths of the optimal portfolios . Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.
A
tight
R
provide several examples which illustrate that without these conditions, we cannot generally expect continuity to hold
also establish a weak convergence result for the terminal wealths of the optimal portfolios
R
minimum shortfall
minimal expected shortfall (shortfall risk)