Optimal investment for retail investors

We study optimal portfolio decisions for a retail investor that faces a strictly positive transaction cost 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 for a variety of real‐world cost structures faced by retail investors. We find that the cost structure has a strong effect on the qualitative shape of the no‐trading region and optimal strategies.