This paper extends the traditional group self-annuitisation framework by explicitly incorporating mortality heterogeneity among participants. Heterogeneity stems from multiple factors that lead individuals to age at different paces, despite being born in the same year. Ageing is modelled as a finite-state continuous-time Markov process where each state represents a distinct phase of physiological deterioration, and transitions capture the stochastic progression towards death. Benefits are differentiated by ageing state and, after issue, they are dynamically adjusted in response to the realised evolution of both ageing and mortality. Our design is novel in its use of the Markov ageing framework within a risk-sharing scheme and in how benefits are updated. Indeed, both benefits and their respective adjustment coefficients are state-specific. Through the explicit modelling of cross-subsidies across states, the design ensures that actuarial equivalence between benefits and available resources is preserved both at the pool level and within each ageing state. However, we find that benefit adjustments based on actuarial equivalence may display undesirable patterns in some ageing classes, when their size shrinks substantially; this happens, in particular, in the younger ageing states, which are likely to empty out. To contrast such effects, we introduce a design preserving a target level of differentiation across states that mitigates the unfavourable impact of a declining size for younger ages. In our analysis, we point out that such a design (which is desirable in many respects) implies solidarity effects across states. Such effects can be identified by comparing benefit amounts under the two assumptions (i.e., benefits adjusted according to actuarial equivalence or so to preserve a predefined level of differentiation). The proposed framework is tested using Australian mortality data.

In classical credibility theory, estimation is typically limited to the hypothetical mean, restricting its use for premium principles that depend on higher-order moments. To address this, we develop a credibility-based framework for estimating the process variance under both known and unknown hypothetical means and apply these estimators to a broad class of variance-related premium principles, including the expected value, variance, standard deviation, and modified-variance principles. The estimators are derived via constrained linear projection techniques, minimizing the mean squared error between the estimator and the true process variance. Explicit formulas are obtained that are optimal among affine transformations of the data. The proposed estimators exhibit desirable statistical properties, including conditional unbiasedness, consistency, mean squared error convergence, and asymptotic normality. Numerical studies demonstrate their favorable convergence behavior, and an empirical analysis with real insurance data highlights their practical relevance. This framework extends Bühlmann’s classical credibility theory to second-moment estimation while remaining computationally tractable and requiring only mild moment conditions, without specifying the population or prior distributions.