相关论文: On the representation of weakly maxitive monetary …
In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables…
We consider a generic diffusion on the 1D torus and give a simple representation formula for the large deviation rate functional of its invariant probability measure, in the limit of vanishing noise. Previously, this rate functional had…
The Shilkret integral with respect to a completely maxitive capacity is fully determined by a possibility distribution. In this paper, we introduce a weaker topological form of maxitivity and show that under this assumption the Shilkret…
In the rate-distortion function and the Maximum Entropy (ME) method, Minimum Mutual In-formation (MMI) distributions and ME distributions are expressed by Bayes-like formulas, in-cluding Negative Exponential Functions (NEFs) and partition…
We generalise the Gartner-Ellis theorem of large deviations theory. Our results allow us to derive large deviation type results in stochastic optimal control from the convergence of generalised logarithmic moment generating functions. They…
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
The rate function for large deviations of the finite time Lyapunov exponent for the derived process in TM corresponding to a stochastic differential equation in M is related, via the Gartner-Ellis theorem, to the p-th moment Lyapunov…
We study the non-parametric isotonic regression problem for bivariate elicitable functionals that are given as an elicitable univariate functional and its Bayes risk. Prominent examples for functionals of this type are (mean, variance) and…
Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
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,…
Let $(\mu_{\alpha})$ be a net of Radon sub-probability measures on the real line, and $(t_{\alpha})$ be a net in $]0,+\infty[$ converging to 0. Assuming that the generalized log-moment generating function $L(\lambda)$ exists for all…
We obtain a first order extension of the large deviation estimates in the G\"{a}rtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order…
It is perhaps not widely recognized that certain common notions of distance between probability measures have an alternative dual interpretation which compares corresponding functionals against suitable families of test functions. This dual…
We construct a pathwise calculus for functionals of integer-valued measures and use it to derive an martingale representation formula with respect to a large class of integer-valued random measures. Using these results, we extend the…
We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such…
In this paper, we study properties of certain risk measures associated with acceptance sets. These sets describe regulatory preconditions that have to be fulfilled by financial institutions to pass a given acceptance test. If the financial…
We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for…
We study the asymptotic behaviour of sequences of multivariate random variables representing the number of occurrences of a given set of symbols in a word of length $n$ generated at random according to a rational stochastic model. Assuming…
The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the…