Discrete compound Poisson process with curved boundaries: Polynomial structures and recur\,sions

DOI10.1007/s11009-006-9014-2zbMath1122.60043OpenAlexW2044607007MaRDI QIDQ2644299

Claude Lefèvre

Publication date: 10 September 2007

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-006-9014-2

zbMATH Keywords

order statisticscompound Poisson processrisk theoryrecursive methodsfirst crossing timegeneralized Appell polynomialsdam modellinggeneralized Abel-Gontcharoff polynomials

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Stopping times; optimal stopping problems; gambling theory (60G40)

Related Items

Finite-time ruin probabilities for discrete, possibly dependent, claim severities ⋮ Boundary crossing of order statistics point processes ⋮ An operator property of the distribution of a nonhomogeneous Poisson process with applications ⋮ On the evaluation of finite-time ruin probabilities in a dependent risk model ⋮ Ruin problems for a discrete time risk model with non-homogeneous conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sheffer polynomials for computing exact Kolmogorov-Smirnov and Renyi type distributions
• An improved finite-time ruin probability formula and its \(Mathematica\) implementation.
• Some recent results on the distributions of stopping times of compound Poisson processes with linear boundaries
• Polynomial structures in order statistics distributions
• Contributions to the theory of first-exit times of some compound processes in queueing theory
• A nonhomogeneous risk model for insurance
• On the first meeting or crossing of two independent trajectories for some counting processes.
• Some properties of polynomial sets of type zero
• The Supremum and Infimum of the Poisson Process
• A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes
• Distributions of stopping times for poisson processes with linear boundaries
• Distribution of first-exit times for empirical counting and poisson processes with moving boundaries
• Distributions of stopping times for compound poisson processes with positive jumps and linear boundaries
• The probability of ruin in finite time with discrete claim size distribution
• Absorption and first-passage times for a compound Poisson process in a general upper boundary
• Problèmes de ruine en théorie du risque à temps discret avec horizon fini
• Numerical Finite-Time Ruin Probabilities by the Picard-Lef vre Formula
• Abel-Gontcharoff pseudopolynomials and the exact final outcome of SIR epidemic models (III)
• First crossing of basic counting processes with lower non-linear boundaries: A unified approach through pseudopolynomials (I)
• UPPER FIRST-EXIT TIMES OF COMPOUND POISSON PROCESSES REVISITED
• A finite-time ruin probability formula for continuous claim severities
• The distribution of general final state random variables for stochastic epidemic models