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Deep stochastic optimization in finance

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Abstract

This paper outlines, and through stylized examples evaluates a novel and highly effective computational technique in quantitative finance. Empirical Risk Minimization (ERM) and neural networks are key to this approach. Powerful open source optimization libraries allow for efficient implementations of this algorithm making it viable in high-dimensional structures. The free-boundary problems related to American and Bermudan options showcase both the power and the potential difficulties that specific applications may face. The impact of the size of the training data is studied in a simplified Merton type problem. The classical option hedging problem exemplifies the need of market generators or large number of simulations.

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Notes

  1. Although we believe that the following parameters are not crucial for replicating our results (because they were not tuned), we list them here for completeness: batch size: 512; optimizer: Adam with the Flux default parameters \((\eta , \beta _1, \beta _2) = (0.001, 0.9, 0.999)\); and the number of epochs was a fixed value for which the training error of a typical run had plateaued.

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Acknowledgements

Research of the second and the third authors was partially supported by the National Science Foundation Grant DMS 2106462.

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Authors and Affiliations

  1. Questrom School of Business, Boston University, Boston, MA, 02215, USA

    A. Max Reppen

  2. Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, 08540, USA

    H. Mete Soner & Valentin Tissot-Daguette

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  1. A. Max Reppen
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  2. H. Mete Soner
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  3. Valentin Tissot-Daguette
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Correspondence to H. Mete Soner.

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Reppen, A.M., Soner, H.M. & Tissot-Daguette, V. Deep stochastic optimization in finance. Digit Finance 5, 91–111 (2023). https://doi.org/10.1007/s42521-022-00074-6

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