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We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…

Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p…

Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating…

Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…

This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…

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…

Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or…

A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…

Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the…

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…

The interconnectedness of financial institutions affects instability and credit crises. To quantify systemic risk we introduce here the PD model, a dynamic model that combines credit risk techniques with a contagion mechanism on the network…

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…

We discuss the systemic risk implied by the interbank exposures reconstructed with the maximum entropy method. The maximum entropy method severely underestimates the risk of interbank contagion by assuming a fully connected network, while…

Combining efficient and safe control for safety-critical systems is challenging. Robust methods may be overly conservative, whereas probabilistic controllers require a trade-off between efficiency and safety. In this work, we propose a…

In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…

This paper introduces and studies factor risk measures. While risk measures only rely on the distribution of a loss random variable, in many cases risk needs to be measured relative to some major factors. In this paper, we introduce a…

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…

Network-theoretic tools contribute to understanding real-world system dynamics, e.g., in wildlife conservation, epidemics, and power outages. Network visualization helps illustrate structural heterogeneity; however, details about…

This paper firstly addresses the problem of risk assessment under false data injection attacks on uncertain control systems. We consider an adversary with complete system knowledge, injecting stealthy false data into an uncertain control…