Retrospective reserves and bonus in multi-state life insurance

Specialeforsvar: William Joakim Pallesen

Titel: Retrospective reserves and bonus in multi-state life insurance

Abstract: In with-profit life insurance, the customer pays some predetermined premiums and then he or she will receive some benefits later on. In order to make sure the insurance company can pay its liabilities, it has to make some prudent assumptions about the interest rate and the transition intensities. These assumptions set the foundation for determining what the customer as a minimum will receive in payout. The fact that they are prudent means that the insurance company would expect a surplus at some point. This paper introduces ways of how to handle the surplus.
First we look at the situation without policyholder behavior as described in (Bruhn and Lollike, 2020). Here we introduce ways on how to project the surplus and the savings account. These projections can be used to predict the future profits for different dividends strategies which can be very helpful when deciding which dividend strategy to use. Afterwards, we will introduce
policyholder behavior as in the article (Falden and Nyegaard, 2021). This article includes the option to surrender and convert to free policy. The article by Debbie Falden and Anna Nyegaard introduces 1 dividend strategy with 3 different interest rates. On the other hand, in Bruhn and Lolike’s paper only 1 interest rate is used for 3 different dividend strategies. We will combine
the two approaches from the articles and come up with a numerical example. This means we will look at 2 different dividends strategies in 3 different interest rate scenarios and come up with some conclusions based on the results.

Vejleder: Jesper Lund Pedersen
Censor:   Kenneth Bruhn, Edlund