Dealing with Drift Uncertainty: A Bayesian Learning Approach

One of the main challenges investors have to face is model uncertainty. Typically, the dynamic of the assets is modeled using two parameters: the drift vector and the covariance matrix, which are both uncertain. Since the variance/covariance parameter is assumed to be estimated with a certain level of confidence, we focus on drift uncertainty in this paper. Building on filtering techniques and learning methods, we use a Bayesian learning approach to solve the Markowitz problem and provide a simple and practical procedure to implement optimal strategy. To illustrate the value added of using the optimal Bayesian learning strategy, we compare it with an optimal nonlearning strategy that keeps the drift constant at all times. In order to emphasize the prevalence of the Bayesian learning strategy above the nonlearning one in different situations, we experiment three different investment universes: indices of various asset classes, currencies and smart beta strategies.

A class of finite-dimensional numerically solvable McKean-Vlasov control problems

We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress-later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.

A Climate-scale Satellite Record for Carbon Monoxide: The MOPITT Version 7 Product

The MOPITT (“Measurements of Pollution in the Troposphere”) satellite instrument has been making observations of atmospheric carbon monoxide since 2000. Recent enhancements to the MOPITT retrieval algorithm have resulted in the release of the Version 7 (V7) product. Improvements include (1) representation of growing atmospheric concentrations of N2O, (2) use of meteorological fields from the MERRA-2 reanalysis for the entire MOPITT mission (instead of MERRA), (3) use of the MODIS Collection 6 cloud mask product (instead of Collection 5), (4) a new strategy for radiance bias correction, and (5) an improved method for calibrating MOPITT’s NIR radiances. Statistical comparisons of V7 validation results with corresponding V6 results are presented, using aircraft in-situ measurements as the reference. Clear improvements are demonstrated for V7 products with respect to overall retrieval biases, bias variability, and bias drift uncertainty.