Forward robust portfolio selection: The binomial case

Abstract

We introduce a new approach for optimal portfolio choice under model ambiguity by incorporating predictable forward preferences in the framework of Angoshtari et al. [2]. The investor reassesses and revises the model ambiguity set incrementally in time while, also, updating his risk preferences forward in time. This dynamic alignment of preferences and ambiguity updating results in time-consistent policies and provides a richer, more accurate learning setting. For each investment period, the investor solves a worst-case portfolio optimization over possible market models, which are represented via a Wasserstein neighborhood centered at a binomial distribution. Duality methods from Gao and Kleywegt [10]; Blanchet and Murthy [8] are used to solve the optimization problem over a suitable set of measures, yielding an explicit optimal portfolio in the linear case. We analyze the case of linear and quadratic utilities, and provide numerical results.

Keywords

Forward robust portfolio selection / Binomial case / Optimal portfolio / Forward performance processes / Linear utilities / Quadratic utilities / Robust forward performance criteria

Acknowledgements

The author would like to thank T. Zariphopoulou for fruitful comments and suggestions.

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