Related papers: Efficient Simulation and Conditional Functional Li…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to MLE become…
We consider a multi-step algorithm for the computation of the historical expected shortfall such as defined by the Basel Minimum Capital Requirements for Market Risk. At each step of the algorithm, we use Monte Carlo simulations to reduce…
We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…
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,…
We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…
Numerical Generalized Randomized Hamiltonian Monte Carlo is introduced, as a robust, easy to use and computationally fast alternative to conventional Markov chain Monte Carlo methods for continuous target distributions. A wide class of…
This paper establishes the functional convergence of the Extreme Nelson--Aalen and Extreme Kaplan--Meier estimators, which are designed to capture the heavy-tailed behaviour of censored losses. The resulting limit representations can be…
We consider the task of assessing the righthand tail of an insurer's loss distribution for some specified period, such as a year. We present and analyse six different approaches: four upper bounds, and two approximations. We examine these…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
Multilevel Splitting methods, also called Sequential Monte-Carlo or \emph{Subset Simulation}, are widely used methods for estimating extreme probabilities of the form $P[S(\mathbf{U}) > q]$ where $S$ is a deterministic real-valued function…
We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in…
This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in…
Rare events in non-linear dynamical systems are difficult to sample because of the sensitivity to perturbations of initial conditions and of complex landscapes in phase space. Here we discuss strategies to control these difficulties and…