# American Institute of Mathematical Sciences

April  2006, 2(2): 165-175. doi: 10.3934/jimo.2006.2.165

## Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain interest rate

 1 Department of Statistics, East China Normal University, Shanghai 200062, P.R., China, China

Received  November 2005 Revised  January 2006 Published  April 2006

In this paper, ruin probabilities are examined in a discrete time risk model in which the interest rates follow a Markov chain with a denumerable state space and the net losses(the claim amount minus the premium income) are assumed to have a dependent AR(1) structure. An upper bound for ultimate ruin probability is obtained by martingale approach. Recursive equations for both finite time ruin probabilities and ultimate ruin probability are derived. By integrating the inductive method and the recursive equation, an upper bound is given for both finite time ruin probabilities and ultimate ruin probability.
Citation: Lin Xu, Rongming Wang. Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain interest rate. Journal of Industrial & Management Optimization, 2006, 2 (2) : 165-175. doi: 10.3934/jimo.2006.2.165
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