Related papers: The Risk Quadrangle in Optimization: An Overview w…

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…

Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the…

We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the…

Distributional reinforcement learning (RL) is a powerful framework increasingly adopted in safety-critical domains for its ability to optimize risk-sensitive objectives. However, the role of the discount factor is often overlooked, as it is…

The work deals with the risk assessment theory. An unitary risk algorithm is elaborated. The algorithm is based on parallel curves. The basic curve of risk is a hyperbolic curve, obtained as a multiplication between the probability of…

Deep Reinforcement Learning (RL) has considerably advanced over the past decade. At the same time, state-of-the-art RL algorithms require a large computational budget in terms of training time to converge. Recent work has started to…

Provably efficient and robust equilibrium computation in general-sum Markov games remains a core challenge in multi-agent reinforcement learning. Nash equilibrium is computationally intractable in general and brittle due to equilibrium…

This paper studies continuous-time risk-sensitive reinforcement learning (RL) under the entropy-regularized, exploratory diffusion process formulation with the exponential-form objective. The risk-sensitive objective arises either as the…

In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following…

We establish the first axiomatic theory for diversification indices using six intuitive axioms: non-negativity, location invariance, scale invariance, rationality, normalization, and continuity. The unique class of indices satisfying these…

Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in…

Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…

Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve…

In finance, sequential decision problems are often faced, for which reinforcement learning (RL) emerges as a promising tool for optimisation without the need of analytical tractability. However, the objective of classical RL is the expected…

The field of portfolio selection is an active research topic, which combines elements and methodologies from various fields, such as optimization, decision analysis, risk management, data science, forecasting, etc. The modeling and…

R. Tyrell Rockafellar and collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or conditional value-at-risk). These methods have been influential in economics, finance,…

First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges:…

In this paper, we provide extended convolution bounds for the Fr\'{e}chet problem and discuss related implications in quantitative risk management. First, we establish a new form of inequality for the Range-Value-at-Risk (RVaR). Based on…

In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…

Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic…