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In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns…
We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…
We consider two nonparametric estimators for the risk measure of the sum of $n$ i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order $n$. This framework…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
It is often the case that risk assessment and prognostics are viewed as related but separate tasks. This chapter describes a risk-based approach to prognostics that seeks to provide a tighter coupling between risk assessment and fault…
Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…
We survey systemic risks to financial markets and present a high-level description of an algorithm that measures systemic risk in terms of coupled networks.
We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a…
We provide a new algorithm for solving Risk Sensitive Partially Observable Markov Decisions Processes, when the risk is modeled by a utility function, and both the state space and the space of observations is finite. This algorithm is based…
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the…
In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
Risk-sensitive planning aims to identify policies maximizing some tail-focused metrics in Markov Decision Processes (MDPs). Such an optimization task can be very costly for the most widely used and interpretable metrics such as threshold…
Operational risk is challenging to quantify because of the broad range of categories (fraud, technological issues, natural disasters) and the heavy-tailed nature of realized losses. Operational risk modeling requires quantifying how these…
Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds…