Related papers: Rare event simulation for processes generated via …
Value-at-Risk (VaR) estimation at high confidence levels is inherently a rare-event problem and is particularly sensitive to tail behavior and model misspecification. This paper studies the performance of two simulation-based VaR estimation…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty…
This paper considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for e.g. modelling of credit risk. Previous attempts at designing importance sampling algorithms…
Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
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…
This article analyzes and compares two general techniques of rare event simulation for generating paths of Markov processes over fixed time horizons: exponential tilting and stochastic bridge. These two methods allow to accurately compute…
Rare events in the first-passage distributions of jump processes are capable of triggering anomalous reactions or series of events. Estimating their probability is particularly important when the jump probabilities have broad-tailed…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
Article describes the results of the development and using of Rare-Event Monte-Carlo Simulation Algorithms for Dynamic Fault Trees Estimation. For Fault Trees estimation usually analytical methods are used (Minimal Cut sets, Markov Chains,…
We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…
State-of-the-art methods for rare event simulation of non-Markovian models face practical or theoretical limits if observing the event of interest requires prior knowledge or information on the timed behavior of the system. In this paper,…
This paper introduces a new Importance Sampling scheme, called Adaptive Twisted Importance Sampling, which is adequate for the improved estimation of rare event probabilities in he range of moderate deviations pertaining to the empirical…