Goal-based portfolio selection with fixed transaction costs

TL;DR

This paper addresses goal-based portfolio optimization with fixed transaction costs, demonstrating the existence of optimal strategies and revealing complex trading behaviors through numerical analysis.

Contribution

It introduces a stochastic Perron's method approach to characterize the value function and establish optimal strategies under transaction costs.

Findings

Optimal trading regions are complex and non-trivial.

Optimal strategies differ significantly from frictionless cases.

The value function is the unique viscosity solution to the system of inequalities.

Abstract

We study a goal-based portfolio selection problem in which an investor aims to meet multiple financial goals, each with a specific deadline and target amount. Trading the stock incurs a strictly positive transaction cost. Using the stochastic Perron's method, we show that the value function is the unique viscosity solution to a system of quasi-variational inequalities. The existence of an optimal trading strategy and goal funding scheme is established. Numerical results reveal complex optimal trading regions and show that the optimal investment strategy differs substantially from the V-shaped strategy observed in the frictionless case.