Estimating the Discounted Density Function of the Deficit at Ruin in a Risk Model with Barrier Dividend Strategy

In this paper, we study the statistical estimation of the discounted density function of the deficit at ruin in the compound Poisson model with barrier dividend strategy. When both the Poisson intensity for the claim number process and the density function for the individual claim sizes are unknown, we use the COS method to construct the estimator. Under a large sample setting, we derive consistency property of the estimator. We also provide simulation results to verify the effectiveness of this estimation method when the sample size is finite.