One-Shot Individual Claims Reserving

Abstract

Individual claims reserving has not yet become established in actuarial practice. We attribute this to the absence of a satisfactory methodology: existing approaches tend to be either overly complex or insufficiently flexible and robust for practical use. Building on the classical chain-ladder (CL) method, we introduced a new perspective on individual claims reserving in Richman and Wüthrich [arXiv:2602.15385]. This manuscript has sparked considerable discussion within the actuarial community. The aim of the present paper is to continue and deepen that discussion, with the ultimate goal of advancing toward a new standard for micro-level reserving.

Figures (6)

• Figure 1: One-period ahead roll-forward extrapolation to predict the ultimate claims $C_{i,J}$ using the observations $C_{i,I-i}$, $i>I-J$, at time $I$ (for $I=7$ and $J=6$); this figure is taken from PtU.
• Figure 2: Backward (in time) one-shot predictions of the ultimate claims $C_{i,J}$, $i>I-J$, using the 'directly estimated' PtU factors $(\widehat{F}^{\rm CL}_j)_{j=0}^{J-1}$ given in \ref{['PtU CL factor']}: (left-middle-right) correspond to $j-1=J-1=5$, $j-1=4$ and $j-1=3$; this figure is taken from PtU.
• Figure 3: (lhs) Individual cumulative payments $C_{i,j|\nu}$ in the upper triangle $i+j \le I$ (each row is one claim, period $i=4$ has twice as many claims as $i=3$), and (rhs) aggregated cumulative claims $C_{i,j}$ in the upper triangle. Late reportings are illustrated by gray bars in the left-hand side figure.
• Figure 4: Individual RBNS vs. IBNR projection.
• Figure 5: Claims reserves per accident year $i=1,\ldots, 5$ and separated by closed and open claims at the evaluation date $I$ using the linear regression \ref{['linear regression claim status']}.