scholarly journals The Cramér condition for the Curie–Weiss model of SOC

2016 ◽  
Vol 30 (3) ◽  
pp. 401-431 ◽  
Author(s):  
Matthias Gorny
Keyword(s):  
Cramer Condition ◽  
Cramér Condition

scholarly journals The Pólya-Aeppli process and ruin problems

2004 ◽  
Vol 2004 (3) ◽  
pp. 221-234 ◽  
Author(s):  
Leda D. Minkova
Keyword(s):  
Poisson Process ◽  
Ruin Probability ◽  
Counting Process ◽  
Risk Model ◽  
Classical Risk Model ◽  
Homogeneous Poisson Process ◽  
Cramer Condition ◽  
Cramér Condition

The Pólya-Aeppli process as a generalization of the homogeneous Poisson process is defined. We consider the risk model in which the counting process is the Pólya-Aeppli process. It is called a Pólya-Aeppli risk model. The problem of finding the ruin probability and the Cramér-Lundberg approximation is studied. The Cramér condition and the Lundberg exponent are defined. Finally, the comparison between the Pélya-Aeppli risk model and the corresponding classical risk model is given.

scholarly journals Stability of the exit time for Lévy processes

2011 ◽  
Vol 43 (03) ◽  
pp. 712-734
Author(s):  
Philip S. Griffin ◽  
Ross A. Maller
Keyword(s):  
Lévy Process ◽  
Exit Time ◽  
Passage Time ◽  
Risk Process ◽  
Levy Processes ◽  
Levy Process ◽  
Conditional Stability ◽  
Insurance Risk ◽  
Cramer Condition ◽  
Cramér Condition

This paper is concerned with the behaviour of a Lévy process when it crosses over a positive level, u, starting from 0, both as u becomes large and as u becomes small. Our main focus is on the time, τ u , it takes the process to transit above the level, and in particular, on the stability of this passage time; thus, essentially, whether or not τ u behaves linearly as u ↓ 0 or u → ∞. We also consider the conditional stability of τ u when the process drifts to -∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cramér condition.

scholarly journals Large deviation results for a U-statistical sum with product kernel

2001 ◽  
Vol 63 (1) ◽  
pp. 151-165 ◽  
Author(s):  
Y. V. Borovskikh ◽  
N. C. weber
Keyword(s):  
Large Deviation ◽  
Product Kernel ◽  
Cramer Condition ◽  
Cramér Condition

Large deviation theorems are proved for non-degenerate U-statistical sums of degree m with kernel h (x1, …, xm) = x1 … xm under the Cramér condition and under the Linnik condition. The method of proof uses truncation and the contraction technique.

scholarly journals Stability of the exit time for Lévy processes

2011 ◽  
Vol 43 (3) ◽  
pp. 712-734 ◽  
Author(s):  
Philip S. Griffin ◽  
Ross A. Maller
Keyword(s):  
Lévy Process ◽  
Exit Time ◽  
Passage Time ◽  
Risk Process ◽  
Levy Processes ◽  
Levy Process ◽  
Conditional Stability ◽  
Insurance Risk ◽  
Cramer Condition ◽  
Cramér Condition

This paper is concerned with the behaviour of a Lévy process when it crosses over a positive level, u, starting from 0, both as u becomes large and as u becomes small. Our main focus is on the time, τu, it takes the process to transit above the level, and in particular, on the stability of this passage time; thus, essentially, whether or not τu behaves linearly as u ↓ 0 or u → ∞. We also consider the conditional stability of τu when the process drifts to -∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cramér condition.

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