an:02192297
Zbl 1122.91340
Cai, Jun; Dickson, David C. M.
Ruin probabilities with a Markov chain interest model
EN
Insur. Math. Econ. 35, No. 3, 513-525 (2004).
0167-6687
2004
j
91B30 60J20
Discrete time risk process; Markov chain; Ruin probability; Rate of interest; Lundberg's inequality; Regularly varying tail; Heavy-tailed distribution
Summary: Finite and infinite time ruin probabilities in a discrete time risk process with a Markov chain interest model are studied. Recursive and integral equations for the ruin probabilities are given. When interest rates are non-negative, generalized Lundberg inequalities for the infinite time ruin probability are derived by inductive and martingale approaches. When interest rates can be negative and loss distributions have regularly varying tails, asymptotic formulas for the finite time ruin probability are given by an inductive approach on the recursive equations.