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A deep learning algorithm for optimal investment strategies

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  • Daeyung Gim
  • Hyungbin Park

Abstract

This paper treats the Merton problem how to invest in safe assets and risky assets to maximize an investor's utility, given by investment opportunities modeled by a $d$-dimensional state process. The problem is represented by a partial differential equation with optimizing term: the Hamilton-Jacobi-Bellman equation. The main purpose of this paper is to solve partial differential equations derived from the Hamilton-Jacobi-Bellman equations with a deep learning algorithm: the Deep Galerkin method, first suggested by Sirignano and Spiliopoulos (2018). We then apply the algorithm to get the solution of the PDE based on some model settings and compare with the one from the finite difference method.

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  • Daeyung Gim & Hyungbin Park, 2021. "A deep learning algorithm for optimal investment strategies," Papers 2101.12387, arXiv.org.
    • Handle: RePEc:arx:papers:2101.12387
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    References listed on IDEAS

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    1. Albina Danilova & Michael Monoyios & Andrew Ng, 2009. "Optimal investment with inside information and parameter uncertainty," Papers 0911.3117, arXiv.org, revised Feb 2010.
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    5. Ali Al-Aradi & Adolfo Correia & Danilo Naiff & Gabriel Jardim & Yuri Saporito, 2018. "Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning," Papers 1811.08782, arXiv.org.
    6. Gilles Pagès & Thibaut Montes & Vincent Lemaire, 2020. "Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization," Working Papers hal-02434232, HAL.
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    10. Zongxia Liang & Ming Ma, 2020. "Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1035-1072, July.
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