On asymptotically efficient simulation of ruin probabilities in a Markovian environment

DOI10.1080/03461238.1992.10413897zbMath0755.62080OpenAlexW4256465461MaRDI QIDQ4025275

Harri Nyrhinen, Tapani Lehtonen

Publication date: 18 February 1993

Published in: Scandinavian Actuarial Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03461238.1992.10413897

zbMATH Keywords

importance samplingasymptotic efficiencyMonte Carlo simulationlevel crossingMarkov additive processruin probabilitieslarge deviations criterionsimulation kernels

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Monte Carlo methods (65C05) Large deviations (60F10) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (9)

Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors ⋮ On the typical level crossing time and path ⋮ Large Deviations for a Damped Telegraph Process ⋮ On asymptotically efficient simulation of large deviation probabilities ⋮ Efficient importance sampling for Monte Carlo evaluation of exceedance probabilities ⋮ Compound binomial risk model in a Markovian environment ⋮ Dynamic importance sampling for uniformly recurrent Markov chains ⋮ On Monte Carlo estimation of large deviations probabilities ⋮ Large Deviation Results for Wave Governed Random Motions Driven by Semi-Markov Processes

Cites Work

• Markov additive processes. I: Eigenvalue properties and limit theorems
• Markov additive processes. II: Large deviations
• The ruin problem for finite Markov chains
• Importance sampling in the Monte Carlo study of sequential tests
• Non-negative matrices and Markov chains.
• Limit theorems for first-passage times in linear and non-linear renewal theory
• Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains
• Large deviations theory and efficient simulation of excessive backlogs in a GI/GI/m queue
• Convex Analysis

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