Simple Bounds for Utility Maximization with Small Transaction Costs

2018/02/16 by Bruno Bouchard, Bouchard, Bruno, Johannes Muhle‐Karbe +1
Economics, Econometrics and Finance · #60H07 #91G10 #91G80 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR)

paper · pdf · doi:10.48550/arxiv.1802.06120

openalex publication_date 2018/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Using elementary arguments, we show how to derive L_p-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.

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