A Polynomial-Affine Approximation for Dynamic Portfolio Choice

Yichen Zhu (), Marcos Escobar-Anel () and Matt Davison ()
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Yichen Zhu: Western University
Marcos Escobar-Anel: Western University
Matt Davison: Western University
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

Computational Economics, 2023, vol. 62, issue 3, No 14, 1177-1213

Abstract: Abstract 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.

Keywords: Dynamic programming; Quadratic–Affine processes; Expected utility; Portfolio optimization; Stochastic interest rates; Stochastic volatility; 49M25; 49N90; 60G99; 91-08 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10614-022-10297-9

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