Related papers: Mean-Covariance Robust Risk Measurement
In this paper, we propose a distributionally robust safety verification method for Markov decision processes where only an ambiguous transition kernel is available instead of the precise transition kernel. We define the ambiguity set around…
In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the…
This work aims to deal with the optimal allocation instability problem of Markowitz's modern portfolio theory in high dimensionality. We propose a combined strategy that considers covariance matrix estimators from Random Matrix Theory~(RMT)…
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…
This work presents a distributionally robust Kalman filter to address uncertainties in noise covariance matrices and predicted covariance estimates. We adopt a distributionally robust formulation using bicausal optimal transport to…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
Selecting the optimal Markowitz porfolio depends on estimating the covariance matrix of the returns of $N$ assets from $T$ periods of historical data. Problematically, $N$ is typically of the same order as $T$, which makes the sample…
Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…
We briefly review the approach to optimization of portfolios according to the theory of Markowitz and propose a further modification that can improve the outcome of the optimization process. The modification takes account of the entropic…
Markowitz's optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random…
We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit…
We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach…
We propose a distributional framework for benchmarking socio-technical risks of foundation models with quantified statistical significance. Our approach hinges on a new statistical relative testing based on first and second order stochastic…
It is well known that the out-of-sample performance of Markowitz's mean-variance portfolio criterion can be negatively affected by estimation errors in the mean and covariance. In this paper we address the problem by regularizing the…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable but also various economic scenarios. Motivated by this…
As machine learning models become increasingly prevalent in critical decision-making models and systems in fields like finance, healthcare, etc., ensuring their robustness against adversarial attacks and changes in the input data is…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
Risk control and optimal diversification constitute a major focus in the finance and insurance industries as well as, more or less consciously, in our everyday life. We present a discussion of the characterization of risks and of the…