scholarly journals On importance sampling with mixtures for random walks with heavy tails

2012 ◽  
Vol 22 (2) ◽  
pp. 1-21 ◽  
Author(s):  
Henrik Hult ◽  
Jens Svensson
Keyword(s):  
Random Walks ◽  
Importance Sampling ◽  
Heavy Tails

RANDOM WALKS WITH HEAVY TAILS AND LIMIT THEOREMS FOR BRANCHING PROCESSES WITH MIGRATION AND IMMIGRATION

2012 ◽  
Vol 12 (01) ◽  
pp. 1150007 ◽  
Author(s):  
YAQIN FENG ◽  
STANISLAV MOLCHANOV ◽  
JOSEPH WHITMEYER
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
Heavy Tails ◽  
Stochastic Dynamics ◽  
Branching Processes ◽  
Spatial Dynamics ◽  
Limiting Distributions ◽  
Central Result

The central result of this paper is the existence of limiting distributions for two classes of critical homogeneous-in-space branching processes with heavy tails spatial dynamics in dimension d = 2. In dimension d ≥ 3, the same results are true without any special assumptions on the underlying (non-degenerated) stochastic dynamics.

scholarly journals Rare-Event Simulation of Heavy-Tailed Random Walks by Sequential Importance Sampling and Resampling

2012 ◽  
Vol 44 (04) ◽  
pp. 1173-1196
Author(s):  
Hock Peng Chan ◽  
Shaojie Deng ◽  
Tze-Leung Lai
Keyword(s):  
Random Walks ◽  
Importance Sampling ◽  
Rare Event ◽  
Sequential Importance Sampling ◽  
New Approach ◽  
Martingale Representation ◽  
Event Simulation ◽  
Markov Random ◽  
Heavy Tailed ◽  
Asymptotically Efficient

We introduce a new approach to simulating rare events for Markov random walks with heavy-tailed increments. This approach involves sequential importance sampling and resampling, and uses a martingale representation of the corresponding estimate of the rare-event probability to show that it is unbiased and to bound its variance. By choosing the importance measures and resampling weights suitably, it is shown how this approach can yield asymptotically efficient Monte Carlo estimates.

scholarly journals Rare-Event Simulation of Heavy-Tailed Random Walks by Sequential Importance Sampling and Resampling

2012 ◽  
Vol 44 (4) ◽  
pp. 1173-1196 ◽  
Author(s):  
Hock Peng Chan ◽  
Shaojie Deng ◽  
Tze-Leung Lai
Keyword(s):  
Random Walks ◽  
Importance Sampling ◽  
Rare Event ◽  
Sequential Importance Sampling ◽  
New Approach ◽  
Martingale Representation ◽  
Event Simulation ◽  
Markov Random ◽  
Heavy Tailed ◽  
Asymptotically Efficient

We introduce a new approach to simulating rare events for Markov random walks with heavy-tailed increments. This approach involves sequential importance sampling and resampling, and uses a martingale representation of the corresponding estimate of the rare-event probability to show that it is unbiased and to bound its variance. By choosing the importance measures and resampling weights suitably, it is shown how this approach can yield asymptotically efficient Monte Carlo estimates.

Importance Sampling for Credit Portfolio Risk with Risk Factors Having t-Copula

2017 ◽  
Vol 16 (04) ◽  
pp. 1101-1124 ◽  
Author(s):  
Rongda Chen ◽  
Ze Wang ◽  
Lean Yu
Keyword(s):  
Risk Factors ◽  
Importance Sampling ◽  
Variance Reduction ◽  
Heavy Tails ◽  
Risk Measure ◽  
Optimization Technique ◽  
Tail Probability ◽  
Portfolio Risk ◽  
Marquardt Algorithm ◽  
Credit Portfolio

This paper proposes an efficient simulation method for calculating credit portfolio risk when risk factors have a heavy-tailed distributions. In modeling heavy tails, its features of return on underlying asset are captured by multivariate [Formula: see text]-Copula. Moreover, we develop a three-step importance sampling (IS) procedure in the [Formula: see text]-copula credit portfolio risk measure model for further variance reduction. Simultaneously, we apply the Levenberg–Marquardt algorithm associated with nonlinear optimization technique to solve the problem that estimates the mean-shift vector of the systematic risk factors after the probability measure change. Numerical results show that those methods developed in the [Formula: see text]-copula model can produce large variance reduction relative to the plain Monte Carlo method, to estimate more accurately tail probability of credit portfolio loss distribution.

scholarly journals Importance sampling of heavy-tailed iterated random functions

2018 ◽  
Vol 50 (3) ◽  
pp. 805-832
Author(s):  
Bohan Chen ◽  
Chang-Han Rhee ◽  
Bert Zwart
Keyword(s):  
Markov Chain ◽  
Stationary Solution ◽  
Importance Sampling ◽  
Heavy Tails ◽  
Lipschitz Functions ◽  
Natural Conditions ◽  
Random Functions ◽  
State Dependent ◽  
Large Jump ◽  
Heavy Tailed

AbstractWe consider the stationary solutionZof the Markov chain {Zn}n∈ℕdefined byZn+1=ψn+1(Zn), where {ψn}n∈ℕis a sequence of independent and identically distributed random Lipschitz functions. We estimate the probability of the event {Z>x} whenxis large, and develop a state-dependent importance sampling estimator under a set of assumptions on ψnsuch that, for largex, the event {Z>x} is governed by a single large jump. Under natural conditions, we show that our estimator is strongly efficient. Special attention is paid to a class of perpetuities with heavy tails.

Sign in / Sign up

Export Citation Format

Share Document