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http://dx.doi.org/10.4134/JKMS.j210168

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)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.2, 2022 , pp. 311-335 More about this Journal
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.
Keywords
Merton problem; optimal investment; deep learning algorithm; deep Galerkin method;
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