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(1)

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MC std error

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(13)

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22 L4i?| @|U?} TThL@Uit E

D )i@h @??@* @ih@}i _i?t|) ET@h@4i|iht @t @MLi

50 100 150 200 250 300

0.002 0.004 0.006 0.008 0.01

Geometric 3 Moment 2 Moment Monte-Carlo Density

(15)

22 L4i?| @|U?} TThL@Uit Ee

D )i@h @??@* t@? U@** ihhLht ET@h@4i|iht @t @MLi

100 200 300 400 500 600

-1 -0.5 0.5

MC-3MM MC-2MM

(16)
(17)

2 hh@?<t i|L_ E2

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 TThL 4@|i E CmC @t *L}?Lh4@*c | T@h@4i|iht _iTi?_?} L?

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2 t c M| ULLti T@h@4i|iht Lu ECmC @t UL?t|@?|t ihtt C 4ihU@* ?|i}h@|L? t|** hi^hi_c M| 4U u@t|ih

TThL 4@|i ??ih ?|i}h@* .dE gnmCo M) d.EmC gon @?_ hiT*@Ui *Lih ?|i}h@|L? *4| EC ' f M) C ' C G .EmC ' g 4ihU@* ?|i}h@|L? ?L *L?}ih hi^hi_ Eih) u@t|

4@?) L|ih @TThL 4@|L?t @hi

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AiLhi|U@**) ?L| UL?ih}i?|c M| 4@) ?L| 4@||ih

(18)

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D )i@h @??@* t@? U@** ihhLhtG hh@? t L4i?| 4@|U?}

100 200 300 400 500 600

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MC-Curran A MC-Curran P MC-3MM

MC-2MM

(19)

2 hh@?<t i|L_ Ee

D )i@h @??@* t@? U@** ihhLhtG L4T@htL? Lu ThiUti ihtt @TThL 4@|i uLh4t Lu hh@?<t 4i|L_

100 200 300 400 500 600

0.02 0.04 0.06 0.08 0.1 0.12

MC-Curran A MC-Curran P

(20)
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2e #i?t|) ih|hM@|L? AiU?^it E2

Nt?} ThLTih|it Lu |i 6Lhih |h@?tuLh4G

(22)

2e #i?t|) ih|hM@|L? AiU?^it E

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(23)

2e #i?t|) ih|hM@|L? AiU?^it Ee

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6Lh t@?tc |i 4i|L_ @TTi@ht RE?c uLh M@t!i|t RE?

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D )i@h @??@* t@? U@** ihhLhtG i?} a t L4i?| 4@|U?}

100 200 300 400 500 600

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MC-NJ MC-3MM MC-2MM

(25)

2e #i?t|) ih|hM@|L? AiU?^it ES

D )i@h @??@* t@? U@** ihhLhtG i?} a t hh@?

100 200 300 400 500 600

-0.05 0.05 0.1

MC-Curran A MC-Curran P MC-NJ

(26)

2D L?L*|L? i|L_

Ai L?*) _i|ih4?t|U@**) UL?ih}i?| |iU?^i uLh t@? LT|L?t E@hih** @?_ *i*Lc bbf

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Lc UL4T*i|i t^@hit |L i*4?@|i uLh4@* K _iTi?_i?Ui

(29)

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W? |i 3 4i@thic |i + @i 4i@?t D3 @?_ UL@h@?Uit E| + \cG

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(30)
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`i U@? |?! Lu |t @t |i R?@|h@* i T@?tL? 4i|L_ uLh @ _ithi_ _i?t|) @hL?_ @ EULhhi*@|i_ ?Lh4@* _i?t|)

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(32)

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REsG .dEe@ e&no ' S.de%od_nco e&d_o REs2G .dEe@ e&no '

S

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At t ?_iTi?_i?| Lu i|ih |i LT|L? t t@? Lh @ M@t!i|

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, |i?tL? |L 5, t t|h@}|uLh@h_ E4*|@h@|i @TThL 4@|L? 6Lh € i_ ?|tc hit*|t @hi t4*@h |L |Lti @MLi( uLh € i_ ?L|L?@*c UL?i |) ULhhiU|L?t @TTi@h

(33)

e 4ihU@* L?ih}i?Ui hLTih|it

D )i@h @??@* t@? U@** ihhLhtG ih|hM@|L? t ThiUti hh@?

100 200 300 400 500 600

-0.02 -0.015 -0.01 -0.005 0.005

MC-Curran P MC-perturb 5M MC-perturb 4M MC-perturb 3M MC-perturb 2M

(34)

e 4ihU@* L?ih}i?Ui hLTih|it E2

D )i@h @??@* t@? U@** ihhLhtG ih|hM@|L? t ThiUti hh@?

100 150 200 250 300

-0.02 -0.015 -0.01 -0.005 0.005

MC-Curran P MC-perturb 5M MC-perturb 4M MC-perturb 3M MC-perturb 2M

(35)

e 4ihU@* L?ih}i?Ui hLTih|it E

D )i@hc D UL4TL?i?| i^@**)i}|i_ M@t!i| U@** Ej ' ffc 4c ' ffc L|ih T@h@4i|iht @t MiuLhiG L?|i @h*L t|@?_@h_ ihhLh t t|h!i

100 200 300 400 500

0.001 0.002 0.003 0.004

MC errors

(36)

e 4ihU@* L?ih}i?Ui hLTih|it Ee

D )i@h M@t!i| U@** ihhLhtG i?} a t L4i?| 4@|U?}

100 200 300 400 500

-0.15 -0.1 -0.05 0.05

MC-NJ MC-3MM MC-2MM

(37)

e 4ihU@* L?ih}i?Ui hLTih|it ED

D )i@h M@t!i| U@** ihhLhtG ih|hM@|L? t ThiUti hh@?

100 200 300 400 500

-0.2 -0.15 -0.1 -0.05 0.05 0.1 0.15

MC-Curran HEL MC-perturb 5M MC-perturb 4M MC-perturb 3M MC-perturb 2M

(38)

D AiLhi|U@* L?ih}i?Ui hLTih|it

4ihU@* UL?ih}i?Ui ThLTih|it *LL! ^|i }LL_ uLh t@?tc ii? uLh u@h*) i |hi4i T@h@4i|iht

6Lh M@t!i|tc itTiU@**) | } L*@|*|it%*L ULhhi*@|L?tc Thi*4?@h) ? 4ihU@* hit*|t t}}it| UL?ih}i?Ui t 4U i@!ih

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`i<hi ?L| thi i|ih |i 4i|L_ @t @ €?|i h@_t Lu UL?ih}i?Ui Lh i|ih |<t t4T*) @t)4T|L|U

(39)

S L?U*tL?t

?i 4i|L_ uLh i T@?_?} |i U@h@U|iht|U u?U|L? Lu @h|4i|U E@?_ L|ih @ih@}it @t Mii? _ihi_

`*i |i @TThL@U t 4Lt| U*Lti*) hi*@|i_ |L i@h*ih U@h@U|iht|U u?U|L? i T@?tL? |iU?^itc 4U Lu |t ?Li*|) *it ? |i ti Lu @ hiuihi?Ui _t|hM|L? ULhhi*@|i_ |L |i UL4TL?i?|t Lu |i @ih@}i

5?Ui |i }iL4i|hU @ih@}i t @ ?@|h@* U@?__@|i uLh |i hiuihi?Ui _t|hM|L?c Lh 4i|L_ @*tL |it ? ?Ui*) | |@| ti}4i?| Lu |i t@? LT|L? *|ih@|hi |@| i T*L|t |i U*Lti hi*@|L?tT Mi|ii? }iL4i|hU @?_ @h|4i|U @ih@}it

Ai @TThL@U *i@_t |L ?||i ULhhiU|L?t |L |i U@h@U|iht|U u?U|L? @?_ LT|L? @*it W? T@h|U*@hc i Ui**i?| UL?|hL* Lih 4L4i?|t t ThL_i_

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