Related papers: Extreme Measures in Continuous Time Conic Finace
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…
We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show…
We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…
This paper investigates a new class of equations called measure functional differential equations with state-dependent delays. We establish the existence and uniqueness of solutions and present a discussion concerning the appropriate phase…
We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such…
Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim…
Consider an ergodic measure preserving dynamical system $(T,X,\mu)$, and an observable $\phi:X\to\mathbb{R}$. For the time series $X_n(x)=\phi(T^{n}(x))$, we establish limit laws for the maximum process $M_n=\max_{k\leq n}X_k$ in the case…
Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a…
We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage…
Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…
The bounds for absolute moments of order statistics are established. Let $X_1,\dots ,X_n$ be independent identically distributed real-valued random variables and let $X_{1:n}\le \dots \le X_{n:n}$ be the corresponding order statistics. The…
Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…