One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model
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 wit...
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2021-08-01
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Online Access: | https://www.mdpi.com/2227-9091/9/9/152 |
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doaj-7cc5ffae3a694af39345da8930c648112021-09-26T01:20:18ZengMDPI AGRisks2227-90912021-08-01915215210.3390/risks9090152One-Year and Ultimate Reserve Risk in Mack Chain Ladder ModelMarcin Szatkowski0Łukasz Delong1Institute of Econometrics, SGH Warsaw School of Economics, Niepodległości 162, 02-554 Warsaw, PolandInstitute of Econometrics, SGH Warsaw School of Economics, Niepodległości 162, 02-554 Warsaw, PolandWe 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.https://www.mdpi.com/2227-9091/9/9/152one-year riskultimate riskreserve riskemergence patternMack Chain Ladder |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Marcin Szatkowski Łukasz Delong |
spellingShingle |
Marcin Szatkowski Łukasz Delong One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model Risks one-year risk ultimate risk reserve risk emergence pattern Mack Chain Ladder |
author_facet |
Marcin Szatkowski Łukasz Delong |
author_sort |
Marcin Szatkowski |
title |
One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model |
title_short |
One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model |
title_full |
One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model |
title_fullStr |
One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model |
title_full_unstemmed |
One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model |
title_sort |
one-year and ultimate reserve risk in mack chain ladder model |
publisher |
MDPI AG |
series |
Risks |
issn |
2227-9091 |
publishDate |
2021-08-01 |
description |
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. |
topic |
one-year risk ultimate risk reserve risk emergence pattern Mack Chain Ladder |
url |
https://www.mdpi.com/2227-9091/9/9/152 |
work_keys_str_mv |
AT marcinszatkowski oneyearandultimatereserveriskinmackchainladdermodel AT łukaszdelong oneyearandultimatereserveriskinmackchainladdermodel |
_version_ |
1716869156310089728 |