Ruin probabilities with a Markov chain interest model

Abstract 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.

[1]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[3]  O. Bunke.  Feller, F.: An Introduction to Probability Theory and its Applications, Vol. II, John Wiley & Sons, Inc., New York‐London‐Sydney, 1966. XVIII + 626 S., 3 Abb., 2 Tab., Preis $ 12,00 , 1969 .

[4]  Gordon E. Willmot,et al.  Lundberg approximations for compound distributions with insurance applications , 2001 .

[5]  Hailiang Yang.  Ruin theory in a financial corporation model with credit risk , 2003 .

[6]  MARTINGALE METHOD FOR RUIN PROBABILITY IN AN AUTOREGRESSIVE MODEL WITH CONSTANT INTEREST RATE , 2003, Probability in the Engineering and Informational Sciences.

[7]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[8]  Jun Cai,et al.  DISCRETE TIME RISK MODELS UNDER RATES OF INTEREST , 2002, Probability in the Engineering and Informational Sciences.

[9]  J. Grandell.  Aspects of Risk Theory , 1991 .

[10]  Qihe Tang,et al.  Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tai , 2003 .

[11]  H. Nyrhinen,et al.  Finite and infinite time ruin probabilities in a stochastic economic environment , 2001 .

[12]  G. Willmot,et al.  Lundberg inequalities for renewal equations , 2001, Advances in Applied Probability.

[13]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[14]  Moshe Shaked,et al.  Stochastic orders and their applications , 1994 .

[15]  Jun Cai,et al.  Ruin probabilities with dependent rates of interest , 2002, Journal of Applied Probability.

[16]  H. Nyrhinen,et al.  On the ruin probabilities in a general economic environment , 1999 .

[17]  Hailiang Yang,et al.  Non-exponential Bounds for Ruin Probability with Interest Effect Included , 1999 .