Rare event simulation techniques

Abstract

We discuss rare event simulation techniques based on state-dependent importance sampling. Classical examples and counter-examples are shown to illustrate the reach and limitations of the state-independent approach. State-dependent techniques are helpful to deal with these limitations. These techniques can be applied to both light and heavy tailed systems and often are based on subsolutions to an associated Isaacs equation and on Lyapunov bounds.

Evaluation of the Probability of Functional Failure of a Redundant System by Importance Sampling Method

“…The unbiasedness of the estimate follows immediately from the formulated algorithm and from formulas (2), (10)- (17).…”

“…Among the variety of the proposed approaches, the most significant directions of study are the importance sampling technique [6][7][8], analytical-statistical method [9][10][11][12][13], multilevel splitting method [14], etc. The methods of fast simulation of the probabilities of rare events are reviewed in [15][16][17].…”

Monte Carlo Methods for Portfolio Credit Risk

“…The rare-event behavior of heavy-tailed random variables is considerably different from the behavior of light-tailed random variables. The theory of rare-event simulation for heavy tails is reviewed in Asmussen and Glynn [2007] and Blanchet and Lam [2011]. Sometimes rare events can happen in more than one way.…”

Diffusion Approximations of the Ruin Probability for the Insurer–Reinsurer Model Driven by a Renewal Process

“…Variance reduction techniques can improve this situation. In this context, we mention importance sampling techniques, where the idea is to sample after an exponential tilt of the probability measure Blanchet and Lam (2011);Collamore (2002). Andersen (1957) in a paper to the 1957 International Congress of actuaries in New York proposed a generalization of the classical risk process.…”