Finite-time Ruin Probabilities For Risk Models With Dependent Heavy-tailed Claims

At the core of risk theory, ruin probability is always a research hot spot in the field of mathematical finance and actuarial. Relatively, finite-time ruin probability has more practical significance than infinite-time ruin probability, and dependence assumption of the claims is more realistic for insurance practice than independence assumption. In this paper, we consider the finite-time ruin probabilities of two customer-arrival-based risk models with dependent heavy-tailed claims. Asymptotic expressions of the finite-time ruin probabilities are derived after some dependence structures presented. Firstly, we introduce the research background of this paper, customer-arrival-based risk models, and several heavy-tailed distribution families. In addition, we give definitions of three types of dependence structure:asymptotic independence, negative dependence and a dependence structure like negative (or positive) regression dependence (we call it negative regression dependence). Secondly, we consider a customer-arrival-based risk model with asymptotically independent (or negatively dependent) potential claims belonging to the class (?L. Asymptotic expressions of the finite-time ruin probability are derived and proofs of them are given. Finally, we consider a customer-arrival-based risk model with dependent implicit claims. Asymptotic expressions of the finite-time ruin probabilities and proofs of them are given in the case that claims are asymptotically independent (or negatively dependent) and belong to the class (?), and in the case that claims are negatively regression dependent and belong to the class S.