Operational Risk Modeling Analytics phần 1 ppsx

... of excesses 7 .12 TVaR for extreme value distributions 7 .13 Further reading 7 .14 Exercises 17 4 17 5 17 8 17 9 17 9 18 0 18 3 18 7 18 7 19 0 19 1 19 1 19 2 1 94 19 8 19 8 205 205 207 ... Operational risk 1. 1 Introduction 1. 1 .1 Basel 11 - General 1. 1.2 1. 2 Operational risk in insurance 1. 3 The analysis of operational risk 1. 4 Th...

Ngày tải lên: 09/08/2014, 19:22

... PROBABILITY CONCEPTS 200 15 0 2. 10 0 50 0 -50 1 I 0 50 10 0 1 50 200 250 300 X Fig. 2 .10 Excess loss variable -50 I I 0 50 10 0 15 0 200 250 300 X f;g. 2 .11 Left censored ... = 1 /a a -1 a2 + 1 Mode = 0 (-) , if Q > 1, else the mode is at 0 This Page Intentionally Left Blank MOMENTS 37 250 200 50 0 0 20 40 60 80 10 0...

Ngày tải lên: 09/08/2014, 19:22

... binomial. 10 0 -10 1, 10 4, 10 9, 11 3, 11 9, 13 3, 19 8, 209, 307 298 as Poisson mixture, 10 1 extended truncated, 11 0 negative hypergeometric, 19 0 Neyman Type A, 11 3, 12 2, 13 3 normal, ... (a + 12 + 1) [ n=O The gamma function itself can be found from 1 1 1 69 1 + + + + 1 1 12 a 360a3 1, 260~~ 1, 680~~ 1, 188ag 360,360all 15 6aI3 12 2,40...

Ngày tải lên: 09/08/2014, 19:22

... accidents, k automobiles, nk k- 0 1 2 3 4 5 6 7 81- Total 7840 13 17 0 .17 239 0.36 42 0.53 14 1. 33 4 1. 43 4 6.00 1 1. 75 0 94 61 against k. The observed values should ... P(,> -Po PT(z) = 1- Po and pz = - pk k= 1, 2, 1 -Po' (5.5) Then from formula (5.4) pf = (1 -p,")pr, k = 1, 2, . , (5.6) PM(Z) = # (1) +...

Ngày tải lên: 09/08/2014, 19:22

... From this, p = 13 .937 31 and cr2 = 0 .12 263 61. Then In 1, 6 81, 337 - 13 .937 31 [ (0 .12 263 61) 0.5 Pr(S > 1, 6 81, 337) = 1 - Q = 1 - Q (1. 135 913 ) = 0 .12 8. 15 2 MODELS FOR ... 7'5(2)0.042678(0.049787) = 0 .17 916 1, 93 = - 7~5 (1) 0.3 414 21( 0 .17 916 1) + 7'5(2) 0.042678(0 .12 7487) 2 3 3 +- 7.5(3) 0. 010 670(0.04978...

Ngày tải lên: 09/08/2014, 19:22

... fs (s) n = 4,096 fs (s) 0 .11 227 0 .11 8 21 0 .14 470 0 .15 100 0 .14 727 0 .13 194 0 .10 9 41 0.08 518 0.04979 0.07468 0 .11 575 0 .13 256 0 .13 597 0 .12 525 0 .10 558 0.08305 Because the FFT ... distribution Table 6 .14 Data for Exercise 6 .15 0. 013 2 0.0 215 0.02 71 0.0 410 fs(6) THE RECURSIVE METHOD 17 5 The starting value of the recursive sch...

Ngày tải lên: 09/08/2014, 19:22

... copula [ 61] has generator +(u) = -In [I - (1 - u)~] , e 2 1. The Joe copula has the form 11 0 d C(U1, , Ud) = 1- c (1 - Uj)' - n(l-Uj)'] . ir j =1 j =1 Note ... dependence function satisfying 1 A(w) = 1 max [x (1 - w), w (1 - x)] dH(z) for any w E [O, 11 and H is a distribution function on [O, 11 . It turns out t...

Ngày tải lên: 09/08/2014, 19:22

... a( 1, oooa) 14 - - j =1 (800 + X~)~+I ’ 14 l(a) = 14 lna +14 aln1,000- (a+l)~ln(800+xj), j =1 = 14 1na + 96.709~ - (a + 1) 105. 810 , I’(a) = 14 a -1 - 9 .10 1, & = 1. 5383. ... Table 10 .1 Data Set A Number of accidents Number of drivers 0 1 2 3 4 5 or more 81, 714 11 ,306 1, 618 250 40 7 Table 10 .2 Data Set B $27 $82 $11 5...

Ngày tải lên: 09/08/2014, 19:22

... = 10 0 to b. The value of b is determined from 12 (4.8 011 21) '2 ln(b/lOO) 12 (4.8 01 12 1) 12 ~(0 .19 59 51 + In y )13 dY dx s 0.95 = = 1 (4.8 011 21 + 2 )13 =1- [ 4.8 011 21 4.8 011 21 ... 1, 920 0 6,433 2 19 5,2 01 29 2:496,935 243 15 ,558,906 1, 116 52,737,840 3,033 10 6.0 21, 739 4,454 11 5,480,050 4, 418 85 ,11 0,453 3,093 44,366,...

Ngày tải lên: 09/08/2014, 19:22

... 0 .17 13 0 .17 12 X2 1. 4034 0.3 615 0.59 51 0.5947 pValue 0.8436 0.94 81 0.8976 0.7428 Loglikelihood -14 6.063 -14 5.683 -11 3.647 -11 3.647 SBC -14 7.535 -14 8.628 -11 5 .14 5 -11 6.643 X2 61. 913 ... 0 10 3,704 1 14 ,075 2 1, 766 3 255 4 45 5 6 6 2 7+ 0 10 2,629.6 15 ,922.0 1, 235 .1 63.9 2.5 0 .1 0.0 0.0 10 3,723.6 13 ,989.9 1, 857 .1...

Ngày tải lên: 09/08/2014, 19:22