Related papers: Convex Risk Measures based on Divergence
Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a…
We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a `potential' or `objective' function. This allows us to rescale data from different assets (or sources) such that each data…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
I propose a functional on the space of spectral risk measures that quantifies their ``degree of risk aversion''. This quantification formalizes the idea that some risk measures are ``more risk-averse'' than others. I construct the…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
Several variants of reweighted risk functionals, such as focal loss, inverse focal loss, and the Area Under the Risk Coverage Curve (AURC), have been proposed for improving model calibration; yet their theoretical connections to calibration…
Evaluating environmental variables that vary stochastically is the principal topic for designing better environmental management and restoration schemes. Both the upper and lower estimates of these variables, such as water quality indices…
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio…
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
We study a non-concave optimization problem in which a financial company maximizes the expected utility of the surplus under a risk-based regulatory constraint. For this problem, we consider four different prevalent risk constraints…
In this paper, we consider the nonconvex minimization problem of the value-at-risk (VaR) that arises from financial risk analysis. By considering this problem as a special linear program with linear complementarity constraints (a bilevel…
This paper is concerned with the properties of the sets of strategic measures induced by admissible team policies in decentralized stochastic control and the convexity properties in dynamic team problems. To facilitate a convex analytical…
We consider bilevel linear problems, where some parameters are stochastic, and the leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome can be modeled by a random…
We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…
The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for…
In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
We review basic concepts of convex duality, focusing on the very general and supremely useful Fenchel-Rockafellar duality. We summarize how this duality may be applied to a variety of reinforcement learning (RL) settings, including policy…
We consider the problem of stochastic convex optimization with exp-concave losses using Empirical Risk Minimization in a convex class. Answering a question raised in several prior works, we provide a $O( d / n + \log( 1 / \delta) / n )$…