Retrospective Reserves and Bonus with Policyholder Behavior

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.