Application of machine learning with asymptotic expansion to unconstrained optimal portfolio

Makoto Naito and Kohta Takehara ()
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Makoto Naito: Graduate School of Management, Tokyo Metropolitan University, 1-4-1 Marunouchi, Chiyoda-ku, Tokyo 100-0005, Japan
Kohta Takehara: Graduate School of Management, Tokyo Metropolitan University, 1-4-1 Marunouchi, Chiyoda-ku, Tokyo 100-0005, Japan

International Journal of Financial Engineering (IJFE), 2025, vol. 12, issue 03, 1-28

Abstract: This paper proposes a numerical method for solving unconstrained optimal portfolio problems. This method combines an asymptotic expansion method applied to the optimal portfolio problem in complete markets, a technique of reformulating the optimal portfolio problem into a corresponding backward stochastic differential equation (BSDE), and a method for BSDEs using machine learning. Numerical examples show that this method may give a better estimate for the optimal portfolio compared to existing methods.

Keywords: Optimal portfolio problems; stochastic optimal controls; backward stochastic differential equations (BSDEs) (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S2424786325500100

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