Retrospective Reserves and Bonus

Scandinavian Actuarial Journal, DOI: 10.1080/03461238.2020.1809509

38 Pages Posted: 15 Apr 2020 Last revised: 31 Jan 2022

See all articles by Kenneth Bruhn

Kenneth Bruhn

Edlund A/S

Alexander Sevel Lollike

University of Copenhagen; University of Copenhagen

Date Written: January 29, 2022


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.

Keywords: Bonus, Retrospective Reserves, FMA, Dividends, With-profit Insurance

JEL Classification: G22

Suggested Citation

Bruhn, Kenneth and Lollike, Alexander Sevel, Retrospective Reserves and Bonus (January 29, 2022). Scandinavian Actuarial Journal, DOI: 10.1080/03461238.2020.1809509, Available at SSRN: or

Kenneth Bruhn

Edlund A/S ( email )

La Cours Vej 7
Frederiksberg, DK-2000

Alexander Sevel Lollike (Contact Author)

University of Copenhagen ( email )

Nørregade 10
Copenhagen, København DK-1165

University of Copenhagen ( email )

Nørregade 10
Copenhagen, København DK-1165

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