Related papers: On dynamic spectral risk measures, a limit theorem…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…