Convergence of utility functions and convergence of optimal strategies
The author studies in a given quite general complete financial market the stability of the optimal investment-consumption strategy with respect to the choice of the utility function. He considers a sequence of utility that converges pointwise and satisfies a given growth condition. It is assumed for each utility function that the usual conditions for the existence of an optimal strategy are fulfilled. The almost sure as well as \(L^p\)-convergence of the optimal wealth and consumption at each date are proved. The \(L^1\)-convergence of the optimal investment process in the general case and the almost sure convergence in the Markov setting is proved. The results can be seen as robustness properties for the optimal strategies. They permit to obtain an approximate optimal strategy when one has an imperfect estimation of the utility function.
scientific article; zbMATH DE number 2118692