In this paper, we consider a bidimensional risk model with stochastic returns and dependent subexponential claims, in which every main claim may be accompanied by a delayed claim, occurring after an uncertain period of time. The surplus of each business line is allowed to be invested in a portfolio of risk-free assets, and the price process of the investment is modeled by a geometric Lévy process. Meanwhile, we employ a time-claim-dependent structure to describe the dependence among claims and the interarrival times. Some uniform asymptotic formulas for the finite-time ruin probabilities are derived under this structure. Finally, a simulation study is conducted to evaluate the accuracy of the derived results.

In this paper we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The claims are assumed to arrive according to a Poisson process and claims follow a light-tailed distribution, and each loss payment of the claims will be settled with a random period of delay. We obtain asymptotic expressions for the ruin probability by exploiting a connection to Poisson models that are not time homogeneous. A finer asymptotic formula is obtained for the special case of exponentially delayed claims and an exact formula is obtained when the claims are also exponentially distributed.