On the absolute ruin in a map risk model with debit interest
Zhang, Zhimin ; Yang, Hailiang ; Yang, Hu
Adv. in Appl. Probab., Tome 43 (2011) no. 1, p. 77-96 / Harvested from Project Euclid
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In this paper we consider a risk model where claims arrive according to a Markovian arrival process (MAP). When the surplus becomes negative or the insurer is in deficit, the insurer could borrow money at a constant debit interest rate to repay the claims. We derive the integro-differential equations satisfied by the discounted penalty functions and discuss the solutions. A matrix renewal equation is obtained for the discounted penalty function provided that the initial surplus is nonnegative. Based on this matrix renewal equation, we present some asymptotic formulae for the discounted penalty functions when the claim size distributions are heavy tailed.
Publié le : 2011-03-15
Classification:  MAP,  absolute ruin,  discounted penalty function,  matrix renewal equation,  asymptotic,  heavy-tailed distribution,  91B30,  91B70 
@article{1300198513,
     author = {Zhang, Zhimin and Yang, Hailiang and Yang, Hu},
     title = {On the absolute ruin in a map risk model with debit interest},
     journal = {Adv. in Appl. Probab.},
     volume = {43},
     number = {1},
     year = {2011},
     pages = { 77-96},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1300198513}
}

Zhang, Zhimin; Yang, Hailiang; Yang, Hu. On the absolute ruin in a map risk model with debit interest. Adv. in Appl. Probab., Tome 43 (2011) no. 1, pp.  77-96. http://gdmltest.u-ga.fr/item/1300198513/