Stochastic retirement in life insurance
Specialeforsvar: Benjamin Bjørn Emborg
Titel: Stochastic retirement in life insurance - Reserve-dependent point probabilities
Abstract: Classical life insurance mathematics assumes a deterministic retirement time. In this thesis, we include the risk of having retirement as a behavioural option in the valuation of the contract. We include discontinuities in the distribution of the retirement time and introduce reserve dependent point probabilities. First, we derive the mathematical framework using the marked point approach and the hazard measure to arrive at the extended Kolmogorov and Thiele equations. Then, we present models that place us in between incidental and rational policyholder behaviour and exploit these. At last, we demonstrate the impact of reserve-dependent stochastic retirement on the market reserves, in different market interest rate environments, with a numerical case study. Based on the numerical study, we observe the importance of the age distribution and how the average retirement age is moved. Finally, we introduce an optimised model and observe a negative impact on the market value of the contract in all market interest rate environments, which indicates that the company does not reserve enough.
Vejleder: Jesper Lund Pedersen
Censor: Jeppe Woetmann Nielsen, Akademikerpension