Valuation of Participating Life Insurance Liabilities

Abstract

P. LINNEMANNLinnemann P. Valuation of participating life insurance liabilities. Scand. Actuarial J. 2004; 2: 81 -104.Surrender and paid-up states are incorporated in the valuation of guaranteed benefits and payments of a level premium paying life insurance policy.We present different valuation methods and examine to what extent they avoid capitalizing and releasing future loadings which are associated with the payment of future premiums.We demonstrate how to avoid capital being required in the future to cover valuation strains. The paid-up benefit valuation method is being extended so that it does not require the premium basis to be on the safe-side of the valuation basis. We obtain a unification and integration of the level premium and paid-up valuation principles.

Cash flows and policyholder behaviour in the semi-Markov life insurance setup

“…In this paper, the exercise of the options occurs randomly, and a similar approach is taken in Henriksen et al (2013) where the insurance risk and policyholder behaviour is modelled by two separate Markov chains, possibly dependent. Earlier studies of random policyholder behaviour modelling include Linnemann (2003) and Linnemann (2004). In contrast to this is the approach where the surrender occurs rationally, which is studied in Steffensen (2002).…”

Understanding the Death Benefit Switch Option in Universal Life Policies

“…The increasing death benefit consists of the sum of a fixed face value Y and the cash value V t at time t : To focus on the pure effect of the death benefit switch option in increasing universal life policies, our model framework does not account for charges or surrenders. According to a standard actuarial valuation (see, e.g., Bowers et al, 1997; Linnemann, 2004), for annual premium payments paid at the beginning of each year t in which the insured is alive, the cash value is given by the following recursive formula: where V 0 = 0. Calculations are based on the actuarial assumptions of a constant annual interest rate i and probabilities of death according to the mortality table.…”

“…Since a switch from an increasing to a level death benefit does not require additional evidence of insurability, mortality and interest rate assumptions remain the same. The equivalence principle requires the present value of future premium payments to equal the present value of future benefits (see, e.g., Bowers et al, 1997; Linnemann, 2004), such that If the initial single premium V τ exceeds the present value of the future benefits of the new level policy, the annual premium is set to zero. Solving for B (τ) thus yields For simplification purposes, we do not include the scenario where, if the available cash value exceeds the present value of the future benefits, the death benefit amount of a universal life policy might as well be increased to maintain a fair contract.…”

Life Insurance Cash Flows with Policyholder Behavior

“…Here, dA(t, s) is the cash flow from the model in Figure 1, as defined by Equation (2). The market value calculated on the market basis including surrender is denoted V s (t) and is given by:…”

“…The policyholder behavior is modeled as random transitions in a Markov model as in [2,3], and the rationality behind surrender and free policy modeling is thus disregarded. An empirical analysis of policyholder behavior in the German market and further references on policyholder modeling can be found in [4].…”