Retrospective Reserves and Bonus with Policyholder Behavior

Abstract

Legislation imposes insurance companies to project their assets and liabilities. 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 ordinary differential equations of the savings account and the surplus, and we include the policyholder behavior options surrender and conversion to free-policy. The inclusion results in a structure where a system of ordinary differential equations of the savings account and the surplus is non-trivial. We consider a case, where we are able to find accurate ordinary differential equation and suggest an approximation method to project the savings account and the surplus including policyholder behavior in general.

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

JEL Classification: G22