Stochastic modeling of financing longevity risk in pension insurance

Abstract

1 Introduction 11 1.1 Motivation 11 1.2 Pension insurance and riskmanagement 12 1.3 Solvency II 15 1.4 Value-at-Risk (VaR) 18 1.5 Insurancemodeling 19 2 Equity index model 23 2.1 Data on equity returns 23 2.2 Model specification and preliminary estimation 29 2.3 Parameter uncertainty via Markov Chain Monte-Carlo 35 2.4 Simulation of future equity returns 38 3 Bond index model 44 3.1 Mediumtermbond index data 45 3.2 Reviewof interest ratemodeling approaches 48 3.3 Model specification and estimation 51 3.4 Parameter uncertainty 57 4 Mortality model 66 4.1 Introduction 66 4.2 Data 67 4.3 Review of the Lee-Cartermodel 69 4.4 Parameter uncertainty in the Lee-Carter model 73 4.5 Gender-specificmortality 77 4.6 The local bilinearmodel 83 5 Dependence modeling 88 5.1 Introduction 88 5.2 Model structure 90 5.3 Model specification 92 5.4 Simulation 94 6 Pension insurance applications 94 6.1 Introduction 94 6.2 Annuity premium and risk analysis for a cohort aged 65 95 6.3 Annuity premium and risk analysis for multiple cohorts 106 6.4 Annuities fromthe customer's point of view 109 7 Discussion 113 8 Appendix 124 8.1 Model implementation example 124