Ruin Probability in Linear Time Series Model

This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and martingale inequalities to obtain expressions for the ruin probability as well as both expo- nential and non-exponential upper bounds for the ruin probability for an infinite time horizon. Numerical re- sults are included to illustrate the accuracy of the non-exponential bound.