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Simple bounds for utility maximization with small transaction costs

Bouchard, Bruno; Muhle-Karbe, Johannes (2022), Simple bounds for utility maximization with small transaction costs, Stochastic Processes and their Applications, 146, p. 98-113. 10.1016/j.spa.2022.01.008

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Type
Article accepté pour publication ou publié
Date
2022
Nom de la revue
Stochastic Processes and their Applications
Volume
146
Éditeur
Elsevier
Pages
98-113
Identifiant publication
Métadonnées
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Auteur(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Muhle-Karbe, Johannes
Department of Mathematics [Imperial College London]
Résumé (EN)
Using elementary arguments, we show how to derive Lp-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities with bounded risk aversion, these estimates yield lower bounds for the frictional value function, which pave the way for its asymptotic analysis using stability results for viscosity solutions. Using tools from Malliavin calculus, we also derive simple sufficient conditions for the regularity of frictionless optimal trading strategies, the second main ingredient for the asymptotic analysis of small transaction costs.
Mots-clés
Transaction costs; Utility maximization; Asymptotics