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Traditional reinforcement learning (RL) aims to maximize the expected total reward, while the risk of uncertain outcomes needs to be controlled to ensure reliable performance in a risk-averse setting. In this paper, we consider the problem…

Machine Learning · Computer Science 2023-01-18 Xian Yu , Siqian Shen

We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These…

Risk Management · Quantitative Finance 2024-02-05 Marlon Moresco , Mélina Mailhot , Silvana M. Pesenti

The spectral risk has wide applications in machine learning, especially in real-world decision-making, where people are not only concerned with models' average performance. By assigning different weights to the losses of different sample…

Optimization and Control · Mathematics 2024-07-23 Yuze Ge , Rujun Jiang

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We…

Risk Management · Quantitative Finance 2011-05-23 Tomasz R. Bielecki , Igor Cialenco , Zhao Zhang

We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected…

Risk Management · Quantitative Finance 2020-08-04 Marcelo Brutti Righi , Paulo Sergio Ceretta

Large health care data repositories such as electronic health records (EHR) open new opportunities to derive individualized treatment strategies for complicated diseases such as sepsis. In this paper, we consider the problem of estimating…

Statistics Theory · Mathematics 2023-10-03 Nilanjana Laha , Aaron Sonabend-W , Rajarshi Mukherjee , Tianxi Cai

This paper introduces a generalized mean-based C^1-smooth robustness measure over discrete-time signals (D-GMSR) for signal temporal logic (STL) specifications. In conjunction with its C1-smoothness, D-GMSR is proven to be both sound and…

Optimization and Control · Mathematics 2024-05-21 Samet Uzun , Purnanand Elango , Pierre-Loic Garoche , Behcet Acikmese

Previous literature shows that prevalent risk measures such as Value at Risk or Expected Shortfall are ineffective to curb excessive risk-taking by a tail-risk-seeking trader with S-shaped utility function in the context of portfolio…

Portfolio Management · Quantitative Finance 2020-11-09 John Armstrong , Damiano Brigo , Alex S. L. Tse

This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance". In particular, we show that the limit spectral measure…

Analysis of PDEs · Mathematics 2021-05-20 Charles Bertucci , Mérouane Debbah , Jean-Michel Lasry , Pierre-Louis Lions

We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of…

Probability · Mathematics 2008-12-10 Patrick Cheridito , Freddy Delbaen , Michael Kupper

We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional…

Risk Management · Quantitative Finance 2016-09-27 Hannes Hoffmann , Thilo Meyer-Brandis , Gregor Svindland

This paper introduces an innovative framework for the periodic evaluation of defined-contribution pension funds. The performance of the pension fund is evaluated not only at retirement, but also within the interim periods. In contrast to…

Risk Management · Quantitative Finance 2025-08-08 Wanting He , Wenyuan Li , Yunran Wei

This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…

Optimization and Control · Mathematics 2018-09-18 Tao Bian , Zhong-Ping Jiang

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…

Probability · Mathematics 2010-12-30 Jocelyne Bion-Nadal , Magali Kervarec

Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…

Mathematical Finance · Quantitative Finance 2020-01-20 Gabriela Kováčová , Birgit Rudloff

Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement…

Computational Finance · Quantitative Finance 2024-02-26 Andrei Neagu , Frédéric Godin , Clarence Simard , Leila Kosseim

Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…

Optimization and Control · Mathematics 2022-05-03 Rui Gao , Anton J. Kleywegt

Task robust adaptation is a long-standing pursuit in sequential decision-making. Some risk-averse strategies, e.g., the conditional value-at-risk principle, are incorporated in domain randomization or meta reinforcement learning to…

Machine Learning · Computer Science 2025-05-16 Yun Qu , Qi Cheems Wang , Yixiu Mao , Yiqin Lv , Xiangyang Ji

We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…

Mathematical Finance · Quantitative Finance 2026-05-20 Marcelo Righi , Eduardo Horta , Marlon Moresco

We study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost…

Optimization and Control · Mathematics 2025-10-16 Nicole Bäuerle , Alexander Glauner