**Hansjörg Albrecher and Eleni Vatamidou \***

Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, QuartierUNIL-ChamberonneBâtimentExtranef,1015 Lausanne,Switzerland;hansjoerg.albrecher@unil.ch

**\*** Correspondence: eleni.vatamidou@unil.ch

Received: 20 September 2019; Accepted: 8 October 2019; Published: 14 October 2019

**Abstract:** We consider the Sparre Andersen risk process with interclaim times that belong to the class of distributions with rational Laplace transform. We construct error bounds for the ruin probability based on the Pollaczek–Khintchine formula, and develop an efficient algorithm to approximate the ruin probability for completely monotone claim size distributions. Our algorithm improves earlier results and can be tailored towards achieving a predetermined accuracy of the approximation.

**Keywords:** Sparre Andersen model; heavy tails; completely monotone distributions; error bounds; hyperexponential distribution
