Total duration of negative surplus for the risk model with debit interest

This paper investigates the compound Poisson risk model with debit interest. The model assumes that the company is allowed to borrow at some debit interest rate when the surplus turns negative. We obtain the Laplace–Stieltjes transform (LST) of the hitting time of the risk process with constant interest when the initial value is less than the hitting level. By the LST together with the strong Markov property of the model, we obtain the LST of the total duration of negative surplus.