Abstract
This paper considers a delayed claim risk model with stochastic return and Brownian perturbation in which each main claim may be accompanied with a delayed claim occurring after a stochastic period of time, and the price process of the investment portfolio is described as a geometric Lévy process. By means of the asymptotic results for randomly weighted sum of dependent subexponential random variables we obtain some asymptotics for finite-time ruin probability. A simulation study is also performed to check the accuracy of the obtained theoretical result via the crude Monte Carlo method.
Highlights
Consider a renewal risk model with main and delayed claims in which, for each positive integer i, an insurer’s ith main claim Xi occurs at time τi accompanied with a delayed claim Yi occurring at time τi + Di, where Di denotes an uncertain delay time
The price process of the investment portfolio is described by a geometric Lévy process {eRt, t 0}
We study the asymptotic expression for the finite-time ruin probability, which has immediate implications under modern insurance regulatory frameworks such as solvency capital requirement and insurance risk management
Summary
Consider a renewal risk model with main and delayed claims in which, for each positive integer i, an insurer’s ith main claim Xi occurs at time τi accompanied with a delayed claim Yi occurring at time τi + Di, where Di denotes an uncertain delay time. The ruin probabilities of risk model (1) were initially studied by [28], who considered a Poisson accident-number process N (t) and some light-tailed claims and established an exact formula for ψ(x) without perturbation and investment (i.e., δ = 0 and Rt = 0) in (1) by a martingale approach. We continue to seek the asymptotic behavior for the finite-time ruin probability in a more general risk model (1) with subexponential claims, risk-free investment, and diffusion perturbation, where each pair of the main and delayed claims may be interdependent to some extent.
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