BAYESIAN LEARNING FOR THE MARKOWITZ PORTFOLIO SELECTION PROBLEM
Carmine de Franco,
Johann Nicolle and
Huyên Pham
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Carmine de Franco: OSSIAM, Paris, France
Johann Nicolle: OSSIAM, Paris, France2Laboratoire de Probabilités Statistique et Modélisation (LPSM), Paris, France
Huyên Pham: Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Université de Paris, Paris, France
International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 07, 1-40
Abstract:
We study the Markowitz portfolio selection problem with unknown drift vector in the multi-dimensional framework. The prior belief on the uncertain expected rate of return is modeled by an arbitrary probability law, and a Bayesian approach from filtering theory is used to learn the posterior distribution about the drift given the observed market data of the assets. The Bayesian Markowitz problem is then embedded into an auxiliary standard control problem that we characterize by a dynamic programming method and prove the existence and uniqueness of a smooth solution to the related semi-linear partial differential equation (PDE). The optimal Markowitz portfolio strategy is explicitly computed in the case of a Gaussian prior distribution. Finally, we measure the quantitative impact of learning, updating the strategy from observed data, compared to nonlearning, using a constant drift in an uncertain context, and analyze the sensitivity of the value of information with respect to various relevant parameters of our model.
Keywords: Bayesian learning; optimal portfolio; Markowitz problem; portfolio selection (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500377
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