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In financial risk management, Value at Risk (VaR) is widely used to estimate potential portfolio losses. VaR's limitation is its inability to account for the magnitude of losses beyond a certain threshold. Expected Shortfall (ES) addresses…
For many real-world decision-making problems subject to uncertainty, it may be essential to deal with multiple and often conflicting objectives while taking the decision-makers' risk preferences into account. Conditional value-at-risk…
Conditional value-at-risk (CoVaR) is one of the most important measures of systemic risk. It is defined as the high quantile conditional on a related variable being extreme, widely used in the field of quantitative risk management. In this…
Conditional value-at-risk (CVaR) is a prominent risk measure in financial engineering, energy systems, and supply chain management. In these domains, Markov decision processes (MDPs) with a long-run CVaR criterion effectively mitigate cost…
This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and…
We study a first-order primal-dual subgradient method to optimize risk-constrained risk-penalized optimization problems, where risk is modeled via the popular conditional value at risk (CVaR) measure. The algorithm processes independent and…
The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an…
We propose nonparametric estimators for conditional value-at-risk (CVaR) and conditional expected shortfall (CES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning…
The ability to make optimal decisions under uncertainty remains important across a variety of disciplines from portfolio management to power engineering. This generally implies applying some safety margins on uncertain parameters that may…
Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional…
The paper discusses capital allocation using the Euler formula and focuses on the risk measures Value-at-Risk (VaR) and Expected shortfall (ES). Some new results connected to this capital allocation is known. Two examples illustrate that…
Conditional value-at-risk (CVaR) and value-at-risk (VaR) are popular tail-risk measures in finance and insurance industries as well as in highly reliable, safety-critical uncertain environments where often the underlying probability…
A new methodology for incorporating LGD correlation effects into the Basel II risk weight functions is introduced. This methodology is based on modelling of LGD and default event with a single loss variable. The resulting formulas for…
Machine learning (ML) models used in prediction and classification tasks may display performance disparities across population groups determined by sensitive attributes (e.g., race, sex, age). We consider the problem of evaluating the…
Given measurements from sensors and a set of standard forces, an optimization based approach to identify weakness in structures is introduced. The key novelty lies in letting the load and measurements to be random variables. Subsequently…
Risk measures such as Expected Shortfall (ES) and Value-at-Risk (VaR) have been prominent in banking regulation and financial risk management. Motivated by practical considerations in the assessment and management of risks, including…
We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The unknown signal and observation are modeled as random vectors whose joint probability distribution is unknown,…
Conditional Value-at-Risk (CVaR) is a widely used risk-sensitive objective for learning under rare but high-impact losses, yet its statistical behavior under heavy-tailed data remains poorly understood. Unlike expectation-based risk, CVaR…
We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four…
The multi-armed bandit (MAB) problem is a ubiquitous decision-making problem that exemplifies the exploration-exploitation tradeoff. Standard formulations exclude risk in decision making. Risk notably complicates the basic reward-maximising…