Parisian ruin probability - the De Vylder type approximation

The Parisian ruin occurs as the capital of the insurance company is negative longer than a predefined period of time. In this article, we propose a simple and fast technique for calculating the Parisian ruin probability for the Cramer-Lundberg model with arbitrary claims that have the first three moments finite. The introduced method is based on the idea of the De Vylder approximation. We apply the method for various claim distributions and verify its accuracy. Lastly, the method is applied to a model that is fitted to the empirical data.