Abstract
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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 77-96 |
| Journal | Advances in Applied Probability |
| DOIs | |
| Publication status | Published - 2011 |
| Externally published | Yes |