Operational Risk Modeling Analytics phần 6 pdf

... 02 04 0 .6 OB 1 0 02 04 0 .6 08 1 U U Fig. 8.15 BB6 copula density (6 = 2, 6 = 2) Fig. 8. 16 BB6 copula pdf (6 = 2, 6 = 2) It has the form The BB6 copula has ... copula pdf (0 = 0.8) 0 02 04 06 0.8 1 0 02 04 06 08 1 U U fig. 8.9 Joe copula density (0 = 2) ARCHIMEDEAN COPULAS 247 06 06 > c 04 02 0...

Ngày tải lên: 09/08/2014, 19:22

... =z 1 - 6 (185 .6 + 0) ' (1,310 .6 + 6) ' In 0.7 = -0.3 566 75 = a In ln0.2 = -1 .60 9438 = a In 6 - 1 .60 9438 -0.3 566 75 = 4.512338 = Numerical methods can be ... 0.000 06 and 0.00001. The first approximation is - d2Z - . 1 (6. 137 96, 1.3894) - 21 (6. 1379,1.3894) + 1 (6. 13784,1.3894) dP2 (0.000 06) - - -157.71389308198 - 2(...

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... 151 5. 16 Exercises 1 56 6 Aggregate loss models 161 6. 1 Introduction 161 6. 2 Model choices 162 6. 3 The compound model for aggregate losses 163 6. 4 Some analytic results 168 6. 5 Evaluation ... 395 3 96 398 399 4 01 402 407 415 References 417 Index 4 26 viii CONTENTS 6. 6 The recursive method 6. 6.1 Compound frequency models 6. 6.2 Underflow/overjlow p...

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... we focus on risk measures that are coherent. 3.3 TAI L-VA LU E- AT- RISK As a risk measure, Value-& ;Risk is used extensively in financial risk manage- ment of trading risk over a ... Model 6 Consider a sample of size 8 in which the observed data points were 3, 5, 6, 6, 6, 7, 7, and 10. The empirical model then has probability function TAIL- VA L UE-A...

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... [from formula (5.5)] pr = 0.3024 06/ (1-0. 362 887) = 0.47 465 1. Then p; = 0.47 465 1 (3 + i) = 0.2 768 80, pF = 0.2 768 80 (5 + ii) = 0.138440. 76 MODELS FOR THE SIZE OF LOSSES: ... 2' b= The first three recursions yield pi = 0. 362 887 (5 + it) = 0.3024 06, p2 = 0.3024 06 (5 + f f) = 0.1 764 04, p3 = 0.1 764 04 (5 + ii) = 0.0...

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... - 0. 362 887) = 1. 569 580. For the zero-modified random variable, pf = 0 .6 arbitrarily. From (5.4), pr = (1 - 0 .6) (0.3024 06) /(1 - 0. 362 887) = 0.189 860 . Then p? = 0.189 860 (5 ... 3 3 3 92 = -0.853553(0.127488) + -0.1 066 94(0.049787) = 0.179 163 , g3 = "00.853553(0.179 163 ) + -0.1 066 94(0.127488) 3(2) +-0.0 266 74(0.049787) 3(3) = 0.184...

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... distribution Table 6. 14 Data for Exercise 6. 15 0.0132 0.0215 0.0271 0.0410 fs (6) THE RECURSIVE METHOD 175 The starting value of the recursive schemes (6. 13) and (6. 14) is fs(0) = ... can be calculated using (6. 13). The resulting distribution is the '(severity" distribu- tion in (6. 17). A second application of formula (6. 13) in (6. 16) results in the...

Ngày tải lên: 09/08/2014, 19:22

... 0.0003 0.0038 0.02 36 0.0 867 0.1718 0.2293 0.21 56 0.1482 0.0 768 0.0308 0.0098 0.0025 0.0005 0.0001 160 ,944 118,085 86, 8 26 63 ,979 47,245 34, 961 25,9 26 19, 265 14,344 10,702 ... 4,4 96 3,380 2,545 1,920 0 6, 433 2 195,201 29 2:4 96, 935 243 15,558,9 06 1,1 16 52,737,840 3,033 1 06. 021,739 4,454 115,480,050 4,418 85,110,453 3,093 44, 366...

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... 0 565 ,66 4 565 ,708.1 565 ,712.4 565 ,66 1.2 1 68 ,714 68 ,570.0 68 ,575 .6 68,721.2 2 5,177 5,317.2 5,295.9 5,171.7 3 365 334.9 344.0 362 .9 4 24 18.7 20.8 29 .6 5 6 1 .o 1.2 3.0 6+ 0 ... 0. 163 1 0.1713 0.1712 X2 1.4034 0. 361 5 0.5951 0.5947 pValue 0.84 36 0.9481 0.89 76 0.7428 Loglikelihood -1 46. 063 -145 .68 3 -113 .64 7 -113 .64 7 SBC -14...

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... n=O The gamma function itself can be found from 1 1 1 69 1 + + + + 1 1 12a 360 a3 1, 260 ~~ 1 ,68 0~~ 1,188ag 360 , 360 all 156aI3 122,400~~~ + 244,188~~~ 125,400~~~ ' For values ... 57, 66 6 -66 7. 55. Hossack, I., Pollard, J., and Zehnwirth, B. (1983) Introductory Statistics with Applications in General Insurance, Cambridge: Cambridge Univer- sity Press...

Ngày tải lên: 09/08/2014, 19:22