First passage times of general sequences of random vectors: A large deviations approach

DOI10.1016/S0304-4149(98)00056-8zbMath0934.60025MaRDI QIDQ1807272

Jeffrey F. Collamore

Publication date: 18 November 1999

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

large deviation principlefirst passage timeconvex analysis

Mathematics Subject Classification ID

Stopping times; optimal stopping problems; gambling theory (60G40) Large deviations (60F10) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (10)

Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors ⋮ Finite and infinite time ruin probabilities in a stochastic economic environment. ⋮ A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process ⋮ Recursive methods for a multi-dimensional risk process with common shocks ⋮ Power estimates for ruin probabilities ⋮ An extension of a logarithmic form of Cramér's ruin theorem to some FARIMA and related processes ⋮ Uniform asymptotics for ruin probability of a two-dimensional dependent renewal risk model ⋮ A \(2\times 2\) random switching model and its dual risk model ⋮ Ruin probabilities for risk processes in a bipartite network ⋮ Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims

Cites Work

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• Markov additive processes. I: Eigenvalue properties and limit theorems
• Markov additive processes. II: Large deviations
• Hitting probabilities and large deviations
• Large deviations for a general class of random vectors
• Aspects of risk theory
• Large exceedances for multidimensional Lévy processes
• Entropy, a useful concept in risk theory
• Ruin probabilities expressed in terms of ladder height distributions
• Rough descriptions of ruin for a general class of surplus processes
• Rough limit results for level-crossing probabilities
• Large exceedences for uniformly recurrent Markov-additive processes and strong-mixing stationary processes
• Convex Analysis

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