Retrospective reserves and bonus

Retrospective Reserves and Bonus with Policyholder Behavior

“…Bruhn and Lollike (2020) derive differential equations for the state-wise projections of the savings account and the surplus from Definition 2 to use for projection in a given interest rate scenario. The theorem below states the main result of Bruhn and Lollike (2020), and the purpose of this paper is to extend these differential equations to a setup including policyholder behavior.…”

“…A high interest rate results in high dividends in our numerical example; therefore, the projected savings accounts are highest in simulation 3. For the effects of changing the dividend strategy, see Bruhn and Lollike (2020). With these calculations, the insurance company can monitor the development of the insurance contract in various scenarios of the interest rate and, for instance, assess the effects of the chosen dividend strategy.…”

“…The retrospective approach without bonus is studied in Norberg (1991) and studied with bonus in Asmussen and Steffensen (2020). Bruhn and Lollike (2020) also reflect on the retrospective perspective and study retrospective reserves with and without bonus. They model the savings account and the surplus of an insurance contract, and derive differential equations for the state-wise projections.…”

“…This paper serves as an extension to Bruhn and Lollike (2020). The extension resides in the incorporation of the policyholder behavior options surrender and conversion to freepolicy.…”

“…In Section 2, we present the general life insurance setup and the model of the savings account, the surplus, and the dividends. We define the projection of the savings account and the surplus without policyholder behavior and state the results from Bruhn and Lollike (2020) in Section 3. Section 4 extends the setup from Section 2 to include policyholder behavior.…”