Convergence of utility functions and convergence of optimal strategies
type: Item
instance of: scholarly article
title: Convergence of utility functions and convergence of optimal strategies
zbMATH Open document ID: 1052.91047
author: Clotilde Napp
author: Elyès Jouini
published in: Finance and Stochastics
publication date: 2004-11-24T00:00:00Z
full work available at URL: FS 04.pdf
review text: 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.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 2118692
zbMATH Keywords: stability
zbMATH Keywords: financial market
zbMATH Keywords: Brownian motion
zbMATH Keywords: agent's problem
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
OpenAlex ID: W2029102758
DOI: 10.1007/S00780-003-0106-3
description: scientific article; zbMATH DE number 2118692