Abstract
We study a discrete-time portfolio selection problem with partial information and maximum drawdown constraint. Drift uncertainty in the multidimensional framework is modeled by a prior probability distribution. In this Bayesian framework, we derive the dynamic programming equation using an appropriate change of measure, and obtain semi-explicit results in the Gaussian case. The latter case, with a CRRA utility function is completely solved numerically using recent deep learning techniques for stochastic optimal control problems. We emphasize the informative value of the learning strategy versus the non-learning one by providing empirical performance and sensitivity analysis with respect to the uncertainty of the drift. Furthermore, we show numerical evidence of the close relationship between the non-learning strategy and a no short-sale constrained Merton problem, by illustrating the convergence of the former towards the latter as the maximum drawdown constraint vanishes.
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21 June 2022
The original version of the book was inadvertently published with incorrect abstracts in the chapters. This has now been amended.
In addition to this, the affiliation of author Dr. Bertram Tschiderer has been changed to Faculty of Mathematics, University of Vienna in the online version of Chapter 10.
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Franco, C.d., Nicolle, J., Pham, H. (2022). Discrete-Time Portfolio Optimization under Maximum Drawdown Constraint with Partial Information and Deep Learning Resolution. In: Yin, G., Zariphopoulou, T. (eds) Stochastic Analysis, Filtering, and Stochastic Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-98519-6_5
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DOI: https://doi.org/10.1007/978-3-030-98519-6_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-98518-9
Online ISBN: 978-3-030-98519-6
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