Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors

DOI10.1214/aoap/1015961169zbMath1021.65003OpenAlexW2024309638MaRDI QIDQ1872411

Jeffrey F. Collamore

Publication date: 6 May 2003

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1015961169

zbMATH Keywords

importance samplingMonte Carlo methodslarge deviationshitting probabilitiesrare event simulationmultidimensional ruin problem

Mathematics Subject Classification ID

Sampling theory, sample surveys (62D05) Markov processes: estimation; hidden Markov models (62M05) Monte Carlo methods (65C05) Discrete-time Markov processes on general state spaces (60J05) Large deviations (60F10)

Related Items

Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes ⋮ Importance sampling for maxima on trees ⋮ Random recurrence equations and ruin in a Markov-dependent stochastic economic environment ⋮ Recursive methods for a multi-dimensional risk process with common shocks ⋮ Efficient rare-event simulation for perpetuities ⋮ On asymptotically efficient simulation of large deviation probabilities ⋮ A sequential Monte Carlo approach to computing tail probabilities in stochastic models ⋮ Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities ⋮ Minimization of a class of rare event probabilities and buffered probabilities of exceedance ⋮ Efficient importance sampling in ruin problems for multidimensional regularly varying random walks ⋮ The stationary tail asymptotics in the GI/G/1-type queue with countably many background states ⋮ Dynamic importance sampling for uniformly recurrent Markov chains ⋮ Optimal control and dependence modeling of insurance portfolios with Lévy dynamics ⋮ Asymptotic multivariate finite-time ruin probability with statistically dependent heavy-tailed claims ⋮ Asymptotic analysis of risk quantities conditional on ruin for multidimensional heavy-tailed random walks ⋮ Rare event simulation for processes generated via stochastic fixed point equations ⋮ Large deviations and fast simulation in the presence of boundaries.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov additive processes. I: Eigenvalue properties and limit theorems
• Markov additive processes. II: Large deviations
• Hitting probabilities and large deviations
• Markov chains and stochastic stability
• Large deviations of uniformly recurrent Markov additive processes
• Large deviations for vector-valued functionals of a Markov chain: Lower bounds
• Dominating points and the asymptotics of large deviations for random walk on \(R^ r\).
• Time series: theory and methods.
• Importance sampling in the Monte Carlo study of sequential tests
• Large deviation lower bounds for arbitrary additive functionals of a Markov chain
• Counterexamples in importance sampling for large deviations probabilities
• Limit theorems for time and place of the first boundary passage by a multidimensional random walk
• First passage times of general sequences of random vectors: A large deviations approach
• On Monte Carlo estimation of large deviations probabilities
• Large deviations and rare events in the study of stochastic algorithms
• General Irreducible Markov Chains and Non-Negative Operators
• Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains
• Asymptotic evaluation of certain markov process expectations for large time. IV
• Simulating level-crossing probabilities by importance sampling
• On asymptotically efficient simulation of ruin probabilities in a Markovian environment
• On the optimality and stability of exponential twisting in Monte Carlo estimation
• A splitting technique for Harris recurrent Markov chains
• A New Approach to the Limit Theory of Recurrent Markov Chains
• The blind simulation problem and regenerative processes
• Risk theory in a Markovian environment
• Analysis of an importance sampling estimator for tandem queues
• Convex Analysis