scholarly journals The local principle of large deviations for compound Poisson process with catastrophes

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Artem Logachov ◽  
Olga Logachova ◽  
Anatoly Yambartsev
Keyword(s):  
Large Deviations ◽  
Poisson Process ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Local Principle

scholarly journals Large deviations for risk processes with reinsurance

2006 ◽  
Vol 43 (03) ◽  
pp. 713-728 ◽  
Author(s):  
Claudio Macci ◽  
Gabriele Stabile
Keyword(s):  
Large Deviations ◽  
Poisson Process ◽  
Large Deviation ◽  
Compound Poisson Process ◽  
Ruin Probabilities ◽  
Small Claim ◽  
Compound Poisson ◽  
Numerical Example ◽  
Markov Modulated ◽  
Risk Processes

We consider risk processes with reinsurance. A general family of reinsurance contracts is allowed, including proportional and excess-of-loss policies. Claim occurrence is regulated by a classical compound Poisson process or by a Markov-modulated compound Poisson process. We provide some large deviation results concerning these two risk processes in the small-claim case. Finally, we derive the so-called Lundberg estimate for the ruin probabilities and present a numerical example.

scholarly journals Large deviations for risk processes with reinsurance

2006 ◽  
Vol 43 (3) ◽  
pp. 713-728 ◽  
Author(s):  
Claudio Macci ◽  
Gabriele Stabile
Keyword(s):  
Large Deviations ◽  
Poisson Process ◽  
Large Deviation ◽  
Compound Poisson Process ◽  
Ruin Probabilities ◽  
Small Claim ◽  
Compound Poisson ◽  
Numerical Example ◽  
Markov Modulated ◽  
Risk Processes

We consider risk processes with reinsurance. A general family of reinsurance contracts is allowed, including proportional and excess-of-loss policies. Claim occurrence is regulated by a classical compound Poisson process or by a Markov-modulated compound Poisson process. We provide some large deviation results concerning these two risk processes in the small-claim case. Finally, we derive the so-called Lundberg estimate for the ruin probabilities and present a numerical example.

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