Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A DEEP LEARNING ALGORITHM FOR OPTIMAL INVESTMENT STRATEGIES UNDER MERTON'S FRAMEWORK

  • Gim, Daeyung (Division of Derivative Pricing Korea Asset Pricing) ;
  • Park, Hyungbin (Department of Mathematical Sciences and Research Institute of Mathematics Seoul National University)
  • Received : 2021.03.08
  • Accepted : 2021.07.19
  • Published : 2022.03.01
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Abstract

This paper treats Merton's classical portfolio optimization problem for a market participant who invests in safe assets and risky assets to maximize the expected utility. When the state process is a d-dimensional Markov diffusion, this problem is transformed into a problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. The main purpose of this paper is to solve this HJB equation by a deep learning algorithm: the deep Galerkin method, first suggested by J. Sirignano and K. Spiliopoulos. We then apply the algorithm to get the solution to the HJB equation and compare with the result from the finite difference method.

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Acknowledgement

Hyungbin Park was supported by Research Resettlement Fund for the new faculty of Seoul National University, South Korea. In addition, Hyungbin Park was supported by the National Research Foundation of Korea (NRF) grants funded by the Ministry of Science and ICT (No. 2017R1A5A1015626, No. 2018R1C1B5085491 and No. 2021R1C1C1011675) and the Ministry of Education (No. 2019R1A6A1A10073437) through the Basic Science Research Program. Financial support from the Institute for Research in Finance and Economics of Seoul National University is gratefully acknowledged.

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