One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model

Marcin Szatkowski and Łukasz Delong
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Marcin Szatkowski: Institute of Econometrics, SGH Warsaw School of Economics, Niepodległości 162, 02-554 Warsaw, Poland

Risks, 2021, vol. 9, issue 9, 1-29

Abstract: We investigate the relation between one-year reserve risk and ultimate reserve risk in Mack Chain Ladder model in a simulation study. The first goal is to validate the so-called linear emergence pattern formula, which maps the ultimate loss to the one-year loss, in case when we measure the risks with Value-at-Risk. The second goal is to estimate the true emergence pattern of the ultimate loss, i.e., the conditional distribution of the one-year loss given the ultimate loss, from which we can properly derive a risk measure for the one-year horizon from the simulations of ultimate losses. Finally, our third goal is to test if classical actuarial distributions can be used for modelling of the outstanding loss from the ultimate and the one-year perspective. In our simulation study, we investigate several synthetic loss triangles with various duration of the claims development process, volatility, skewness, and distributional assumptions of the individual development factors. We quantify the reserve risks without and with the estimation error of the claims development factors.

Keywords: one-year risk; ultimate risk; reserve risk; emergence pattern; Mack Chain Ladder (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:9:y:2021:i:9:p:152-:d:621142

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