Goal-based portfolio selection with fixed transaction costs

Battle Count: 171

The paper is highly relevant to portfolio management and trading strategy design under transaction costs, which is central to quantitative trading. The finding that optimal strategies differ substantially from the frictionless V-shaped strategy has practical implications for retail investment platforms. However, the paper is primarily theoretical/mathematical rather than directly implementable as a trading algorithm. The numerical results on trading regions and funding ratios provide actionable insights for goal-based portfolio construction.

The theoretical framework requires deep expertise in viscosity solutions, stochastic Perron's method, quasi-variational inequalities, and impulse control theory. The numerical implementation involves solving QVI systems on a 2D state space (bank account and stock holdings) with a triangular grid, penalty schemes, and finite difference methods. The construction of optimal strategies requires careful handling of continuation/intervention regions, goal deadlines, and recursive strategy construction. The proofs span multiple appendices with highly technical arguments.

The paper provides detailed mathematical formulations, parameter settings for numerical experiments (G1=3, G2=6, T1=1, T2=2, w1=1, w2=0.2, r=0, mu=0.3, sigma=0.4, Cmin=0.02, grid sizes, time steps), and references to the numerical algorithm (Azimzadeh 2017). However, no code repository is provided, and the proofs are highly technical requiring expertise in viscosity solutions and stochastic control theory.