scholarly journals Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

2020 ◽  
Vol 121 (9) ◽  
pp. 2086-2105 ◽  
Author(s):  
Nassim Razaaly ◽  
Daan Crommelin ◽  
Pietro Marco Congedo
Keyword(s):  
Importance Sampling ◽  
Efficient Estimation ◽  
Extreme Quantiles ◽  
Adaptive Kriging

scholarly journals Efficient importance sampling in ruin problems for multidimensional regularly varying random walks

2010 ◽  
Vol 47 (2) ◽  
pp. 301-322 ◽  
Author(s):  
Jose Blanchet ◽  
Jingchen Liu
Keyword(s):  
Random Walk ◽  
Importance Sampling ◽  
Mean Squared Error ◽  
First Passage Time ◽  
Passage Time ◽  
Natural Generalization ◽  
Efficient Estimation ◽  
State Dependent ◽  
Negative Drift ◽  
Heavy Tailed

We consider the problem of efficient estimation via simulation of first passage time probabilities for a multidimensional random walk with heavy-tailed increments. In addition to being a natural generalization to the problem of computing ruin probabilities in insurance - in which the focus is the maximum of a one-dimensional random walk with negative drift - this problem captures important features of large deviations for multidimensional heavy-tailed processes (such as the role played by the mean of the process in connection to the location of the target set). We develop a state-dependent importance sampling estimator for this class of multidimensional problems. Then, using techniques based on Lyapunov inequalities, we argue that our estimator is strongly efficient in the sense that the relative mean squared error of our estimator can be made arbitrarily small by increasing the number of replications, uniformly as the probability of interest approaches 0.

scholarly journals Efficient importance sampling in ruin problems for multidimensional regularly varying random walks

2010 ◽  
Vol 47 (02) ◽  
pp. 301-322 ◽  
Author(s):  
Jose Blanchet ◽  
Jingchen Liu
Keyword(s):  
Random Walk ◽  
Importance Sampling ◽  
Mean Squared Error ◽  
First Passage Time ◽  
Passage Time ◽  
Natural Generalization ◽  
Efficient Estimation ◽  
State Dependent ◽  
Negative Drift ◽  
Heavy Tailed

We consider the problem of efficient estimation via simulation of first passage time probabilities for a multidimensional random walk with heavy-tailed increments. In addition to being a natural generalization to the problem of computing ruin probabilities in insurance - in which the focus is the maximum of a one-dimensional random walk with negative drift - this problem captures important features of large deviations for multidimensional heavy-tailed processes (such as the role played by the mean of the process in connection to the location of the target set). We develop a state-dependent importance sampling estimator for this class of multidimensional problems. Then, using techniques based on Lyapunov inequalities, we argue that our estimator is strongly efficient in the sense that the relative mean squared error of our estimator can be made arbitrarily small by increasing the number of replications, uniformly as the probability of interest approaches 0.

Sign in / Sign up

Export Citation Format

Share Document