Stochastic Retirement

Specialeforsvar: Christine Winther

Titel: Stochastic Retirement

Abstract: In life insurance today it is common to use a deterministic retirement age when calculating cash flows. It  as however been noticed that the policyholders retire both later and earlier than the expected deterministic retirement age.
This thesis is written in collaboration with Sampension. All analysis and calculations are based on data delivered by Sampension. In this thesis we will compare three models under strict assumptions to ensure simplicity due to calculation time.
We will only focus on the transition from Active to Retirement in lifelong annuities. The first model is a simplified version of the Markov chain we use today in Sampension where retirement starts at a specific age, 65.5, without jumping to a retirement state.
The second model is a enhanced version of the first model. We will be in the same Markov chain but we will use a linear regression model to estimate the retirement age. The third model is a Markov chain with stochastic retirement. Using Kolmogorow’s backwards equations and the paid up policy technique we construct a three state Markov chain with the state Active, Retired and a dummy state. The state Dead is removed and it’s intensity is added to the interest rate. Using GLM we make a regression model to estimate the intensity µap. Using the results from the regression models we calculate new cash flows to compare with the current model. Surprisingly the two second models were very similar when aggregating the discounted cash flows however they are very distinct the first ten years if we look closer at just one policy. The first and second model have an unnatural cutoff to the left as the estimated retirement age is respectively 5.5 and 6.5 years later than the earliest possible retirement age. The third model solves this issue as we get a probability of retiring at any age.

Vejledere: Mogens Steffensen, Peter Fledelius, Sampension
Censor:     Kenneth Bruhn, Edlund