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In this paper, we consider some dividend problems in the perturbed compound Poisson model under a constant barrier dividend strategy. We approximate the expected present value of dividend payments before ruin and the expected discounted penalty function based on the COS method, and construct some nonparametric estimators by using a random sample on claim number and individual claim sizes. Under a large sample size setting, we perform an error analysis of the estimators. We also provide some simulation results to verify the effectiveness of this estimation method when the sample size is finite.

Consider a risk model in which X1,…, Xn are n potential losses from different risky assets at the terminal time, and θ1,…,θn are n discount factors over the period. In this paper, we establish some asymptotic formulas for the value at risk and conditional tail expectation of the total discounted loss Sn=∑i=1nθiXi of an investment portfolio. We also demonstrate our obtained results through Monte Carlo simulations with asymptotics.

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