When Bayesian learning meets stochastic optimal control : Optimal portfolio choice under drift uncertainty

Olivier Guéant — Univ. Paris 1 Panthéon-Sorbonne (CES)
vendredi 24 mars 2017

We shall present several models addressing optimal portfolio
choice and optimal portfolio transition issues, in which the expected
returns of risky assets are unknown. Our approach is based on a
coupling between Bayesian learning and dynamic programming techniques.
It permits to recover the well-known results of Karatzas and Zhao in
the case of conjugate (Gaussian) priors for the drift distribution,
but also to go beyond the no-friction case, when martingale methods
are no longer available. In particular, we address optimal portfolio
choice in a framework à la Almgren-Chriss and we build therefore a
model in which the agent takes into account in his/her allocation
decision process both the liquidity of assets and the uncertainty with
respect to their expected returns. We also address optimal portfolio
liquidation and optimal portfolio transition problems.

Keywords : Bayesian learning, Hamilton-Jacobi-Bellman, duality, PDE,
portfolio optimization