Retrospective Reserves and Bonus with Policyholder Behavior

Debbie Kusch Falden and Anna Kamille Nyegaard
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Debbie Kusch Falden: Department of Mathematical Science (MATH), University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
Anna Kamille Nyegaard: Department of Mathematical Science (MATH), University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark

Risks, 2021, vol. 9, issue 1, 1-28

Abstract: Legislation imposes insurance companies to project their assets and liabilities in various financial scenarios. Within the setup of with-profit life insurance, we consider retrospective reserves and bonus, and we study projection of balances with and without policyholder behavior. The projection resides in a system of differential equations of the savings account and the surplus, and the policyholder behavior options surrender and conversion to free-policy are included. The inclusion results in a structure where the system of differential equations of the savings account and the surplus is non-trivial. We consider a case where we are able to find accurate differential equations and suggest an approximation method to project the savings account and the surplus, including policyholder behavior, in general. To highlight the practical applications of the results in this paper, we study a numerical example.

Keywords: with-profit life insurance; bonus; surplus; dividends; projection of balances; retrospective reserve; policyholder behavior (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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