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Discrete-Time Portfolio Optimization under Maximum Drawdown Constraint with Partial Information and Deep Learning Resolution

In: Stochastic Analysis, Filtering, and Stochastic Optimization

Author

Listed:
  • Carmine de Franco

    (OSSIAM, 80, Avenue de la Grande Armée)

  • Johann Nicolle

    (LPSM-OSSIAM, 80, Avenue de la Grande Armée)

  • Huyên Pham

    (Université de Paris, Bâtiment Sophie Germain, Case courrier 7012)

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.

Suggested Citation

  • Carmine de Franco & Johann Nicolle & Huyên Pham, 2022. "Discrete-Time Portfolio Optimization under Maximum Drawdown Constraint with Partial Information and Deep Learning Resolution," Springer Books, in: George Yin & Thaleia Zariphopoulou (ed.), Stochastic Analysis, Filtering, and Stochastic Optimization, pages 101-136, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98519-6_5
    DOI: 10.1007/978-3-030-98519-6_5
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