Claim reserving for insurance contracts in line with the International Financial Reporting Standards 17: a new paid-incurred chain approach to risk adjustments

Financial Innovation

Table 8 Parameter estimates recovered from incurred claims data and their corresponding standard errors (SEs)

Development	Bodily injury				Direct compensation				Accident benefit
year	\(\varphi _{j,1}\)	SE (\(\varphi _{j,1}\))	\(\tau _{j,1}\)	SE(\(\tau _{j,1}\))	\(\varphi _{j,2}\)	SE (\(\varphi _{j,2}\))	\(\tau _{j,2}\)	SE (\(\tau _{j,2}\))	\(\varphi _{j,2}\)	SE (\(\varphi _{j,3}\))	\(\tau _{j,3}\)	SE (\(\tau _{j,3}\))
1	0.3637	0.0136	0.0489	0.0009	0.0235	0.0018	0.0065	0.0000	0.2235	0.0227	0.0820	0.0026
2	0.2793	0.0139	0.0480	0.00094	0.0001	0.0002	0.0007	0.0000	0.0776	0.0154	0.0535	0.0012
3	0.1357	0.0084	0.0280	0.0003	0.0000	0.0001	0.0004	0.0000	0.0587	0.0087	0.0289	0.0004
4	0.0591	0.0069	0.0220	0.0002	0.0000	0.0001	0.0005	0.0000	0.0266	0.0029	0.0091	0.0000
5	0.0238	0.0056	0.0169	0.0001	− 0.0001	0.0001	0.0002	0.0000	0.0163	0.0026	0.0078	0.0000
6	0.0105	0.0036	0.0101	0.0001	0.0001	0.0000	0.0001	0.0000	0.0082	0.0026	0.0073	0.0000
7	0.0046	0.0024	0.0063	0.0000	− 0.0001	0.0000	0.0001	0.0000	0.0073	0.0019	0.0049	0.0000
8	0.0037	0.0008	0.0019	0.0000	0.0000	0.0000	0.0001	0.0000	0.0062	0.0015	0.0038	0.0000
9	0.0003	0.0007	0.0015	0.0000	0.0000	0.0000	0.0000	0.0000	0.0048	0.0012	0.0027	0.0000
10	0.0017	0.0010	0.0020	0.0000	0.0000	0.0000	0.0000	0.0000	0.0044	0.0010	0.0021	0.0000
11	− 0.0004	0.0004	0.0006	0.0000	0.0000	0.0000	0.0000	0.0000	0.0019	0.0011	0.0018	0.0000
12	0.0004	0.0002	0.0003	0.0000	0.0000	0.0000	0.0000	0.0000	0.0014	0.0011	0.0016	0.0000
13	− 0.0002	0.0001	0.0001	0.0000	0.0000	0.0000	0.0000	0.0000	− 0.0010	0.0008	0.0008	0.0000
14	0.0006	0.0000	0.0001	0.0000	0.0000	0.0000	0.0000	0.0000	0.0003	0.0000	0.0004	0.0000