1. Department of Actuarial Sciences, The Faculty of Business, Karabük University, Karabük, Turkey
2. Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey
3. Research Centre for Longevity Risk, Faculty of Economics and Business, University of Amsterdam, Amsterdam, Netherlands
4. Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, UK
5. Multi-institution institute, Maxwell Institute for Mathematical Sciences, Edinburgh, UK