Retrospective reserves and bonus

Kenneth Bruhn and Alexander Sevel Lollike

Scandinavian Actuarial Journal, 2021, vol. 2021, issue 6, 457-475

Abstract: Modern legislation has increased the amount of quantities that insurance companies should report in order to prove solvent as well as prudent. More of these quantities require not just simple bookkeeping but a mere projection of the future. In this paper, we provide a solid base for this crystal ball exercise as we derive differential equations for the retrospective reserves of a pension company, in a setting where the surplus and the dividends are modelled. The differential equations rely on dynamics of the stochastic reserve that are affine functions of the stochastic reserve themselves. The retrospective reserves are defined as conditional expected values, given limited information, leading to computational tractable differential equations for the reserves. We wrap up the theoretical part by suggestions for practical use in terms of considering validation of guarantees and discretionary benefits at future time points.

Date: 2021
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DOI: 10.1080/03461238.2020.1809509

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