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.
Highlights
In with-profit life insurance, prudent assumptions about the interest rate and biometric risks at initialization of an insurance contract result in a surplus emerging over time.This surplus belongs to the policyholders and must be paid back in terms of bonus
The paper presents a method for projecting the savings account and the surplus of a life insurance contract including policyholder behavior in various financial scenarios
We present differential equations of the projected savings account and the projected surplus without policyholder behavior, which is the result of Bruhn and Lollike (2020)
Summary
In with-profit life insurance, prudent assumptions about the interest rate and biometric risks at initialization of an insurance contract result in a surplus emerging over time. Steffensen (2006) considers prospective reserves, while we focus on the savings account, which is a retrospective reserve including past bonus, and the surplus of an insurance contract. Bruhn and Lollike (2020) reflect on the retrospective perspective and study retrospective reserves with and without bonus They model the savings account and the surplus of an insurance contract, and derive differential equations for the state-wise projections. We model policyholder behavior as random transitions in the Markov model from the classical life insurance setup extended with surrender and free-policy states as studied in, for instance, (Henriksen et al 2014). We include policyholder behavior options in combination with bonus in our model of the retrospective savings account and surplus, and our approach is based on differential equations of the state-wise projections.
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