A Polynomial-Affine Approximation for Dynamic Portfolio Choice

This paper proposes an efficient and accurate simulation-based method to approximate the solution of a continuous-time dynamic portfolio optimization problem for multi-asset and multi-state variables within expected utility theory. The performance of this methodology is demonstrated in five settings of a risky asset. Closed-form solutions are available for three of these settings-a geometric Brownian motion, a stochastic volatility model, and an exponential Ornstein-Uhlenbeck process-which help assess performance. The fourth setting is a discrete-time vector autoregressive parametrization, which is popular in this area of research. In these cases, we compare our method to at least two relevant benchmarks in the literature: the BGSS methodology of Brandt et al. (Rev Financ Stud 18(3):831-873, 2005) and the SGBM approach of Cong and Oosterlee (Comput Econ 49(3):433-458, 2017) . Our method delivers accurate and fast results for the optimal investment and value function, comparable to analytical solutions. Moreover, it is also significantly faster for a given precision level than the aforementioned competing simulation-based methodologies. Lastly, we explore the solution to a model with mean-reverting SV and interest rate, under full correlation; this last assumption makes it unsolvable in closed-form. Our analysis shows a significant impact of correlation between stock and interest rate on allocation and annualized certainty equivalent rate.