On the distribution of surplus immediately after ruin under interest force and subexponential claims

Abstract

The compound Poisson risk process with a constant interest force is an interesting stochastic model in risk theory. It provides a basic understanding about how investments will affect the ruin probability and related ruin functions. This paper considers the compound Poisson risk model with a constant interest force for an insurance portfolio and studies the distribution of the surplus immediately after ruin under the model. By using the techniques of Kalashnikov and Konstantinides [Kalashnikov, V., Konstantinides, D., 2000. Ruin under interest force and subexponential claims: a simple treatment. Insurance Math. Econ. 27, 145–149] and a formula obtained by Yang and Zhang [Yang, H.L., Zhang, L.H., 2001a. On the distribution of surplus immediately after ruin under interest force. Insurance Math. Econ. 29, 247–255], we give asymptotic formulas of the low and upper bounds for the distribution of the surplus immediately after ruin under subexponential claims. To some extent, we can view our work here as the continuation of the recent important work of Kalashnikov and Konstantinides [Kalashnikov, V., Konstantinides, D., 2000. Ruin under interest force and subexponential claims: a simple treatment. Insurance Math. Econ. 27, 145–149], Yang and Zhang [Yang, H.L., Zhang, L.H., 2001a. On the distribution of surplus immediately after ruin under interest force. Insurance: Mathematics and Economics 29, 247–255] and Konstantinides et al. [Konstantinides, D., Tang, Q.H., Tsitsiashvili, G., 2002. Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails. Insurance Math. Econ. 31, 447–460].