On the application of Thiele's differential equation in life insurance

Biometric worst-case scenarios for multi-state life insurance policies

“…for all t ≥ s and (j, k) ∈ J, then the theory of Norberg (1985), Hoem (1988, Ramlau-Hansen (1988), and Linnemann (1993) yields that…”

“…First, there is the method based on the sum-at-risk, which was developed by Lidstone (1905), Norberg (1985), Hoem (1988), Ramlau-Hansen (1988), and Linnemann (1993). For a given first-order basis with corresponding sums-at-risk for the different transitions, they showed that premiums and reserves are on the safe side if the second-order transition rates are smaller and greater than the firstorder transition rates according as the first-order sums-at-risk are positive and negative, respectively.…”

An Actuarial Analysis of Participating Life Insurance

“…2 155 1.3. Contents of the paper Using Thiele's differential equation and the approaches in Linnemann (1993Linnemann ( , 1994, we develop a simple actuarial model to reveal the intrinsic nature of participating life insurance. It is our aim to illustrate fundamental matters in connection with actuarial reserving of level premium life insurance policies.…”

Sensitivity of life insurance reserves via Markov semigroups

“…We divide the relevant literature in several strands (same typology as in the introduction of Christiansen (2008), see that paper for more exhaustive references). The first is of a qualitative nature where the magnitude of reserve changes cannot be determined as represented by Lidstone (1905) and Norberg (1985) for simple standard contracts, Hoem (1988), Ramlau-Hansen (1988) and Linnemann (1993). The second strand concerns the comparison of several well-defined scenarios as done in Olivieri (2001) and Khalaf-Allah et al (2006).…”