Extend the constrained objective to bootstrap reserve uncertainty

Apply the constrained objective function for development ratios to bootstrap reserve uncertainty estimation so that reserve uncertainty reflects both the observed data and the actuary’s subjective view.

Background

Bootstrap methods are widely used for reserve uncertainty estimation, but manually adjusted development ratios can violate the plug-in principle because the estimates are no longer direct functions of the observed data. The paper’s constrained objective encodes subjective adjustments as formal components of the estimation procedure, potentially preserving the plug-in structure for development-ratio estimation.

The unresolved issue is whether and how this constrained estimation framework should be incorporated into the bootstrap itself, allowing uncertainty estimates to propagate both data-driven variation and the actuary’s declared subjective constraints.