Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point

2024/10/07 by Ashley Davey, Davey, Ashley, Harry Zheng +1 · 1 citation
Computer Science · #Computational Finance (q-fin.CP) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Image Processing and 3D Reconstruction #Machine Learning (stat.ML) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2410.05524

openalex publication_date 2024/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the portfolio optimisation problem where the terminal function is an S-shaped utility applied at the difference between the wealth and a random benchmark process. We develop several numerical methods for solving the problem using deep learning and duality methods. We use deep learning methods to solve the associated Hamilton-Jacobi-Bellman equation for both the primal and dual problems, and the adjoint equation arising from the stochastic maximum principle. We compare the solution of this non-concave problem to that of concavified utility, a random function depending on the benchmark, in both complete and incomplete markets. We give some numerical results for power and log utilities to show the accuracy of the suggested algorithms.

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