Related papers: Extreme-case Range Value-at-Risk under Increasing …
Recently, there has been a surge in interest in safe and robust techniques within reinforcement learning (RL). Current notions of risk in RL fail to capture the potential for systemic failures such as abrupt stoppages from system failures…
The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics…
This paper addresses the problem of estimating, in the presence of random censoring as well as competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in the heavy-tail case.…
We consider statistical Markov Decision Processes where the decision maker is risk averse against model ambiguity. The latter is given by an unknown parameter which influences the transition law and the cost functions. Risk aversion is…
Let $X_1,...,X_n$ be iid random vectors and $f\ge 0$ be a non-negative function. Let also $k(n) = {\rm Argmax}_{i=1,...,n} f(X_i)$. We are interested in the distribution of $X_{k(n)}$ and their limit theorems. In other words, what is the…
The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Analysis of competing risks data is often complicated by the incomplete or selectively missing information on the cause of failure. Standard approaches typically assume that the cause of failure is missing at random (MAR), an assumption…
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…
We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
We propose a new approach, termed Realized Risk Measures (RRM), to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using high-frequency financial data. It extends the Realized Quantile (RQ) approach proposed by Dimitriadis and…
In high-stakes machine learning applications, it is crucial to not only perform well on average, but also when restricted to difficult examples. To address this, we consider the problem of training models in a risk-averse manner. We propose…
This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these…
This paper investigates the regret associated with the Distributionally Robust Control (DRC) strategies used to address multistage optimization problems where the involved probability distributions are not known exactly, but rather are…
We extend the Vasi\v{c}ek loan portfolio model to a setting where liabilities fluctuate randomly and asset values may be subject to systemic jump risk. We derive the probability distribution of the percentage loss of a uniform portfolio and…
In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such…
Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution --…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…