Robust utility maximization under model uncertainty via a penalization approach

Ivan Guo, Nicolas Langrené (), Gregoire Loeper () and Wei Ning
Additional contact information
Ivan Guo: Monash University [Melbourne]
Nicolas Langrené: CSIRO - Commonwealth Scientific and Industrial Research Organisation [Australia]
Gregoire Loeper: Monash University [Melbourne]
Wei Ning: Monash University [Melbourne]

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Abstract: This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We show that this robust optimization process can be interpreted as a two-player zero-sum stochastic differential game. We prove that the value function satisfies the Dynamic Programming Principle and that it is the unique viscosity solution of an associated Hamilton-Jacobi-Bellman-Isaacs equation. We test this robust algorithm on real market data. The results show that robust portfolios generally have higher expected utilities and are more stable under strong market downturns. To solve for the value function, we derive an analytical solution in the logarithmic utility case and obtain accurate numerical approximations in the general case by three methods: finite difference method, Monte Carlo simulation, and Generative Adversarial Networks.

Keywords: robust portfolio optimization; differential games; HJBI equation; Generative adversarial networks; GANs; Monte Carlo (search for similar items in EconPapers)
Date: 2020-08-01
New Economics Papers: this item is included in nep-cmp, nep-gth, nep-ore and nep-upt
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Citations: View citations in EconPapers (5)

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