Related papers: Computational aspects of robust optimized certaint…
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…
There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…
Affine policies (or control) are widely used as a solution approach in dynamic optimization where computing an optimal adjustable solution is usually intractable. While the worst case performance of affine policies can be significantly bad,…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
We investigate the probabilistic feasibility of randomized solutions to two distinct classes of uncertain multi-agent optimization programs. We first assume that only the constraints of the program are affected by uncertainty, while the…
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…
This paper offers a critical view of the "worst-case" approach that is the cornerstone of robust control design. It is our contention that a blind acceptance of worst-case scenarios may lead to designs that are actually more dangerous than…
Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…
The equity risk premium puzzle is that the return on equities has far exceeded the average return on short-term risk-free debt and cannot be explained by conventional representative-agent consumption based equilibrium models. We review a…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal…
In financial markets, accurately measuring the risk of future fluctuations in asset prices is of paramount importance. Studies such as Carr and Madan have shown that the expected value of the quadratic variation of log prices can be…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
Building on ideas from online convex optimization, we propose a general framework for the design of efficient securities markets over very large outcome spaces. The challenge here is computational. In a complete market, in which one…
A fundamental problem in risk management is the robust aggregation of different sources of risk in a situation where little or no data are available to infer information about their dependencies. A popular approach to solving this problem…
The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…
We demonstrate that the recently developed Optimal Uncertainty Quantification (OUQ) theory, combined with recent software enabling fast global solutions of constrained non-convex optimization problems, provides a methodology for rigorous…
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…
In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…