Related papers: Bayesian learning for the Markowitz portfolio sele…
This paper investigates the equilibrium portfolio selection for smooth ambiguity preferences in a continuous-time market. The investor is uncertain about the risky asset's drift term and updates the subjective belief according to the…
We revisit the classic ski rental problem through the lens of Bayesian decision-making and machine-learned predictions. While traditional algorithms minimize worst-case cost without assumptions, and recent learning-augmented approaches…
We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO…
We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…
We study the impact of learning on the optimal policy and the time-to-decision in an infinite-horizon Bayesian sequential decision model with two irreversible alternatives, exit and expansion. In our model, a firm undertakes a small-scale…
We consider the Merton problem of optimizing expected power utility of terminal wealth in the case of an unobservable Markov-modulated drift. What makes the model special is that the agent is allowed to purchase costly expert opinions of…
We present a novel $Q$-learning algorithm tailored to solve distributionally robust Markov decision problems where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball…
We develop and analyze a general technique for learning with an unknown distribution drift. Given a sequence of independent observations from the last $T$ steps of a drifting distribution, our algorithm agnostically learns a family of…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the…
Understanding how adult humans learn non-native speech categories such as tone information has shed novel insights into the mechanisms underlying experience-dependent brain plasticity. Scientists have traditionally examined these questions…
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…
Models of many real-life applications, such as queuing models of communication networks or computing systems, have a countably infinite state-space. Algorithmic and learning procedures that have been developed to produce optimal policies…
The Markowitz mean-variance portfolio optimization model aims to balance expected return and risk when investing. However, there is a significant limitation when solving large portfolio optimization problems efficiently: the large and dense…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
We consider the investor who doesn't trade shares of his portfolio. The investor only observes the current trades made in the market with his securities to estimate the current return, variance, and risks of his unchanged portfolio. We show…
The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
The classical Markowitz mean-variance model uses variance as a risk measure and calculates frontier portfolios in closed form by using standard optimization techniques. For general mean-risk models such closed form optimal portfolios are…
We consider the problem of online learning in the presence of distribution shifts that occur at an unknown rate and of unknown intensity. We derive a new Bayesian online inference approach to simultaneously infer these distribution shifts…