A Neural Network Monte Carlo Approximation for Expected Utility Theory

Yichen Zhu and Marcos Escobar-Anel
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Yichen Zhu: Department of Statistical and Actuarial Sciences, Western University, London, ON N6A5B7, Canada
Marcos Escobar-Anel: Department of Statistical and Actuarial Sciences, Western University, London, ON N6A5B7, Canada
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

JRFM, 2021, vol. 14, issue 7, 1-18

Abstract: This paper proposes an approximation method to create an optimal continuous-time portfolio strategy based on a combination of neural networks and Monte Carlo, named NNMC. This work is motivated by the increasing complexity of continuous-time models and stylized facts reported in the literature. We work within expected utility theory for portfolio selection with constant relative risk aversion utility. The method extends a recursive polynomial exponential approximation framework by adopting neural networks to fit the portfolio value function. We developed two network architectures and explored several activation functions. The methodology was applied on four settings: a 4/2 stochastic volatility (SV) model with two types of market price of risk, a 4/2 model with jumps, and an Ornstein–Uhlenbeck 4/2 model. In only one case, the closed-form solution was available, which helps for comparisons. We report the accuracy of the various settings in terms of optimal strategy, portfolio performance and computational efficiency, highlighting the potential of NNMC to tackle complex dynamic models.

Keywords: neural networks; expected utility theory; CRRA utility; 4/2 stochastic volatility model (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2021
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