(Z-11-3) Table 11.4 (Exercise): computing expected loss and premium, calibrated TVaR distortion.
j
X
ΔX
p
S
X p
S ΔX
g(S)
Δg(S)
X Δg(S)
g(S) ΔX
1
0
1
0.25
0.75
0
0.75
1
0
0
1
2
1
7
0.125
0.625
0.125
4.375
1
0
0
7
3
8
1
0.125
0.5
1
0.5
0.975
0.025
0.2
0.975
4
9
1
0.0625
0.438
0.562
0.438
0.853
0.122
1.097
0.853
5
10
1
0.125
0.312
1.25
0.312
0.609
0.244
2.437
0.609
6
11
79
0.0625
0.25
0.688
19.75
0.487
0.122
1.341
38.511
7
90
8
0.125
0.125
11.25
1
0.244
0.244
21.936
1.95
8
98
2
0.0625
0.0625
6.125
0.125
0.122
0.122
11.943
0.244
9
100
0.0625
0
6.25
0
0.122
12.187
Sum
100
1
27.25
27.25
1
51.142
51.142
(Z-11-4) Table (new) outcomes with assets a=80 (answers only), TVaR distortion.
Limited Loss
Premium
a
80.0
23.625
44.073
(Z-15-1) Table (new): Premium stand-alone by unit, sum, and total, and natural allocation by distortion.
Unit
X1
X2
SoP
Total
Approach
Distortion
Stand-Alone
CCoC
6.306
44.84
51.14
51.14
PH
6.656
45.19
51.85
51.14
Wang
6.992
45.16
52.15
51.14
Dual
7.463
45.01
52.48
51.14
TVaR
8.775
44.36
53.13
51.14
Allocated
CCoC
6.306
44.84
51.14
PH
5.975
45.17
51.14
Wang
6.034
45.11
51.14
Dual
6.225
44.92
51.14
TVaR
7.025
44.12
51.14
(Z-15-2) Table (new): Progression of premium benefit by distortion. Differences between allocated and stand-alone, the implied premium reduction, and the split by unit.