Optimal Investment to Reach a Financial Goal: A Stochastic Control Framework

Battle Count: 50

Highly relevant for institutional investors and robo-advisors focusing on goal-based investing rather than pure mean-variance optimization. It challenges classical Merton portfolio rules by showing that optimal risk exposure can decrease with asset drift and does not vanish with infinite volatility, which is crucial for designing robust goal-reaching strategies.

High complexity due to the need for solving non-linear PDEs (HJB equations) using viscosity solution theory and implementing Howard's algorithm with implicit finite difference methods. Requires strong background in stochastic calculus and numerical analysis.

The paper provides detailed mathematical derivations, algorithm descriptions (Howard's algorithm), and parameter settings for numerical simulations. However, no code repository is explicitly linked in the text provided, requiring re-implementation of the finite difference schemes and policy iteration.