an:05186217
Zbl 1141.91023
Cai, Jun
On the time value of absolute ruin with debit interest
EN
Adv. Appl. Probab. 39, No. 2, 343-359 (2007).
00210555
2007
j
91B30 60K05 91B70
Compound Poisson process; defective renewal equation; key renewal theorem; absolute ruin; deficit at absolute ruin; Gerber-Shiu function; debit interest; subexponential
This paper assumes the classical compound Poisson risk reserve process but allows, in the case of negative values, for borrowing of money at a certain debit interest rate. The insurer has to repay the debts continuously from the premium income. If he fails, absolute ruin occurs. The author studies absolute ruin questions by defining an expected discounted penalty function at absolute ruin, which includes the absolute ruin probability, the Laplace transform of the time to absolute ruin, the deficit at absolute ruin, and further quantities related to absolute ruin.
Bero Roos (Leicester)