Reserve-dependent Management Actions in life insurance
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In a set-up of with-profit life insurance including bonus, we study the calculation of the market reserve, where Management Actions such as investment strategies and bonus allocation strategies depend on the reserve itself. Since the amount of future bonus depends on the retrospective savings account, the introduction of Management Actions that depend on the prospective market reserve results in an entanglement of retrospective and prospective reserves. We study the complications that arise due to the interdependence between retrospective and prospective reserves, and characterize the market reserve by a partial differential equation (PDE). We reduce the dimension of the PDE in the case of linearity, and furthermore, we suggest an approximation of the market reserve based on the forward rate. The quality of the approximation is studied in a numerical example.
Original language | English |
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Journal | Scandinavian Actuarial Journal |
Volume | 2023 |
Issue number | 1 |
Pages (from-to) | 1-19 |
ISSN | 0346-1238 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Funding Information:
This research was funded by Innovation Fund Denmark [award number 7076-00029]. We would like to thank Mogens Steffensen for general comments and discussions during this work, and to thank Christian Furrer and Kristian Buchardt for insightful comments that helped to improve the paper.
Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.
- Bonus, Management Actions, Prospective reserves, With-profit life insurance
Research areas
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