On the Compound Poisson Risk Model with Debit Interest and a Threshold Dividend Strategy

In this paper, a compound Poisson risk model with debit interest and a constant dividend barrier is considered under absolute ruin. When the surplus is below a fixed positive level, the surplus is kept as liquid reserves, which do not earn interest. When the surplus attains the level, the excess of the surplus over the level will receive interest at a constant rate. On the contrary, when the surplus is negative but not too far to zero, the insurer would loan some money from the bank. Integro-differential equations satisfied by the expectation of discounted aggregate dividend payments with certain boundary conditions are obtained. When the claim sizes obey the exponential distribution, explicit solutions are obtained.