Fractional Poisson process: long-range dependence and applications in ruin theory
Biard, Romain ; Saussereau, Bruno
HAL, hal-00831074 / Harvested from HAL
Text on HAL
We study a renewal risk model in which the surplus process of the insurance company is modeled by a compound fractional Poisson process. We establish the long-range dependence property of this non-stationary process. Some results for the ruin probabilities are presented in various assumptions on the distribution of the claim sizes.
Publié le : 2014-07-05
Classification:  long-range dependence,  Fractional Poisson process,  renewal process,  ruin probability,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00831074,
     author = {Biard, Romain and Saussereau, Bruno},
     title = {Fractional Poisson process: long-range dependence and applications in ruin theory},
     journal = {HAL},
     volume = {2014},
     number = {0},
     year = {2014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00831074}
}

Biard, Romain; Saussereau, Bruno. Fractional Poisson process: long-range dependence and applications in ruin theory. HAL, Tome 2014 (2014) no. 0, . http://gdmltest.u-ga.fr/item/hal-00831074/