Optimal Investment for Retail Investors with Floored and Capped Costs

Abstract

We study optimal portfolio decisions for a retail investor that faces proportional costs which are floored and capped at some minimal and maximal cost levels, respectively, in a classical Black-Scholes market. We provide a construction of optimal trading strategies and characterize the value function as the unique viscosity solution of the associated quasi-variational inequalities. Moreover, we numerically investigate the optimal trading regions and find a distinct structure: The no-trading region is vVv-shaped, and all optimal trades for small (large) levels of wealth incur the floored (capped) cost; proportional cost trades occur only in a narrow intermediate wealth regime.

Keywords: Portfolio Optimization, Transaction Costs, Retail Investor

JEL Classification: G11, C61