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Estimate Some Tools Probabilistic in Insurance and Finance

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DEPARTMENT OF MATHEMATICS

      

     

A Thesis Presented For The Degree Of DOCTOR OF SCIENCES

In The Field Of Statistics

BY 

Abdelaziz RASSOUL 

Estimate Some Tools Probabilistic in Insurance and Finance

Examination Committee Members:

Pr.  Brahim   Mezerdi  U. Biskra        Chairman 

Pr.  Abdelhakim   Necir  U. Biskra        Advisor 

Pr.  Hocine      Fellag  U. Tizi‐ouzou      Examinator 

Pr.  Zaher    Mohdeb  U. Constantine          Examinator 

Pr.  Abderrahmane   Yousfate  U. Sidi Bel‐Abbes       Examinator 

Dr.  Djamel   Meraghni  U. Biskra        Examinator 

 

September 20, 2010

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(20)

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(21)

0E84>498= ,8/ -,=4. :<9:0<>40=

0: HI6GI L>I= I=: 8DBBDC 9:QC>I>DCH >C EGD767>A>IN I=:DGN 6C9 >C;:G:C8: HI6I>H I>8H

0E84>498 &2/ =/> * 3= -+66/. >2/ :<9,+,363>C =:+-/ A2/</ 3= >2/

=:+-/ 90 /6/7/8>+<C /@/8>= 3= ++61/,<+ 90 =?,=/>= 90 +8. * 3= + :<9,+

,363>C 7/+=?</ 98

%:I 7: HDB: B:6HJG67A: HE68: 7: I=: G:6A A>C: L>I= I=:

6A<:7G6 D; DG:A>6C DC

0E84>498 &2/ </+6 @+6?/. 0?8->3982 2 ./E8/. 98 3= -+66/.

+ <+8.97 @+<3+,6/ <@ 30 09< +8C % 2& 296.=

0E84>498 &2/ 0?8->398

)M * %2 M& M

3= -+66/. >2/ .3=><3,?>398 0?8->398 -.0 90 >2/ <@2 +8. =?<@3@+6 0?8->398 9< >+36 .3=><3,?>398 3=

)M )M

0E84>498 /> + 8988/1+>3@/ </+6@+6?/. 0?8->398 ;I I /B3=> =?-2

>2+> 09< +66 M

)M

& >

;I9I +8. =?<@3@+6 0?8->398 3=

)M

&

> ;I9I

&2/ 0?8->398 ;I I 3= -+66/. >2/ :<9,+,363>C ./8=3>C 0?8->398 :.0 90 >2/

<@ 2

0E84>498 &2/ <@G= 2 2 26 A3>2 -97798 -.0 22 2 2

3= + E83>/ =/> +</ -+66/. 38./:/8./8> 3./8>3-+66C .3=><3,?>/. 33. 30 09< +8C

6

* 2 26 6 * 2 * 266 9<

M M M6 M M M6

(22)

0E84>498 &2/ /7:3<3-+6 -.0 9< =+7:6/ -.0 90 >2/ =+7:6/ 2 2 26 3= ./E8/. ,C

6M

C

$6 2

)> M 0E84>498 "</0< =>,>4=>4.= &2/ 9<./< =>+>3=>3-= :/<>+38381 >9 + =+7:6/

2 2 26 +</ >2/ 22H +<<+81/. 38 898./-</+=381 9<./< &2/C +</ ./89>/.

,C 26 2 6 266 +8. 09< @ C >2/ <@ 2646 3= -+66/. >2/ @>2

?::/< 9<./< =>+>3=>3- !<./< =>+>3=>3-= =+>3=0C 26 2 6 266 &2?=

26 &$' 2 2 26 +8. 266 & - 2 2 26 0E84>498 =>,>4=>4.= 9< 6 6 666 >2/ =>+>3=>3-

.6

$6 2

62226

3= -+66/. =>+>3=>3- > 3= + 638/+< -97,38+>398= 90 9<./< =>+>3=>3-=

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-=: :BE>G>86A 89; D; I=: H6BEA:2 2 26>H :K6AJ6I:9 JH>C< DG9:G HI6I>HI>8H 6H ;DAADLH

6M

M 26

26 26 M 266 ;DG > C M266

0E84>498 $?,8>460 ,8/ >,46 ;?,8>460 1?8.>498= &2/ ;?+8>36/ 0?8-

>398 90 89; 3= >2/ 1/8/<+63D/. 38@/<=/ 0?8->398 90 ./E8/. ,C

H H $'"%M MM& H A3>2 >2/ -98@/8>398 >2+> >2/ 38E7?7 90 >2/ /7:>C =/> 3= 8 >2/ >2/9<C 90 /B></7/= + 0?8->398 ./89>/. ,C+8. =97/>37/= -+66/. >+36 ;?+8>36/ 0?8->398 3= ?=/. ;?3>/ 90>/8 > 3= ./E8/. ,C

I I

I I

(23)

0: H=6AA H:: >C I=>H H:8I>DC I=: ;JC8I>DC EA6NH 6 GDA: >C :MIG:B: K6AJ: I=:DGN 8DBE6G67A: ID I=: GDA: D; I=: 8=6G68I:G>HI>8 ;JC8I>DC >C I=: I=:DGN D; I=: HI67A:

9>HIG>7JI>DCH

0E84>498 7:4<4.,6 ;?,8>460 ,8/ >,46 ;?,8>460 1?8.>498= &2/ /7 :3<3-+6 9< =+7:6/ ;?+8>36/ 0?8->398 90 >2/ =+7:6/ 2 2 26 3= ./08/. ,C

6H $'"%M 6MH& H 6 7+C ,/ /B:</==/. += + =37:6/ 0?8->398 90 >2/ 9<./< =>+>3=>3-= :/<>+38381 >9 >2/

=+7:6/ 2 2 26 +7/6C A/ 2+@/

6H 2646 09< C

C H C>

C > C 9>/ >2+> 09< E 2686 3= >2/ =+7:6/ ;?+8>36/ 90 9<./< E

0E84>498 >,46 ;?,8>460 :<9.0== /> 26 2 6 266 ,/ >2/

8>2 9<./< =>+>3=>3-= +8.@@C=+>3=0C381@ @C+=C )/ ./

E8/ >2/ >+36 /7:3<3-+6 ;?+8>36/ :<9-/== >9 ,/ >2/ =>9-2+=>3- :<9-/==

264:6

: 0E84>498 &2/ ?::/< 9< <312> /8.:938> 90 -.0 3= ./E8/. += 09669A=

M +,)%M M&

&2/ 69A/< 9< 6/0> /8.:938> 90 -.0 3= ./E8/. += 09669A=

M $'"%M M&

6/+<6CM +8.M </:</=/8> </=:/->3@/6C >2/ 73837?7 +8. 7+B37?7 +>>+38+,6/

@+6?/= 90 >2/ <@ 2 +==9-3+>/. A3>2 !,@39?=6C M 38 -+=/ 90 + 69A/<

?8,9?8./. <@ +8. M 09< +8 ?::/<?8,9?8./. 98/

0E84>498 <9A84,8 79>498 ,8/ <9A84,8 -<4/20 =>9-2+=>3- :<9-/==

%; I& 3= =+3. >9 ,/ + <9A83+8 79>398 9< + )/38/< :<9-/== 30

!

!! ; 2+= 38./:/8./8> +8. =>+>398+<C 38-</7/8>=

!!! 09< /@/<C I ; 3= 89<7+66C .3=><3,?>/. A3>2 7/+8 +8. @+<3+8-/ I 09< =97/ :9=3>3@/ -98=>+8>

(24)

)6G6B:I:G >H @CDLC 6H I=: K6G>6C8: E6G6B:I:G 0=:C I=:

EGD8:HH >H 86AA:9 HI6C96G9 GDLC>6C BDI>DC ,>C8: 6CN GDLC>6C BDI>DC ;86C 6AL6NH 7: 8DCK:GI:9 ID 6 HI6C96G9 GDLC>6C BDI>DC I=GDJ<= I=:

H86A>C<; I=: K6G>6C8: E6G6B:I:G >H D;I:C H:I ID

GDLC>6C BDI>DC ; >H 6 6JHH>6C EGD8:HH L>I= ; 6C9 DK;: ;: I"H 0: 6AHD =6K: I=6I;:>H IH

;DG 6AA IH

%:I %; I & 7: 6 GDLC>6C BDI>DC -=: 8DC9>I>DC6A EGD8:HH

%; I ' &

>H 86AA:9 6 <9A84,8 -<4/20 "I >H 6 6JHH>6C EGD8:HH L>I= B:6C 6C9 8DK6G>6C8: ;JC8I>DC HI H I C 6AI:GC6I>K: 6EEGD68= ID D7I6>C>C<

HJ8= 6 EGD8:HH >H ID H:I

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0E84>498 7:4<4.,6 :<9.0== &2/ /7:3<3-+6 :<9-/== 90 >2/ 33. =+7 :6/ 2 2 26 3= ./E8/. ,C

:6M )

C 6M M M

A2/</ 6 3= >2/ /7:3<3-+6 .3=><3,?>398 0?8->398 ,+=/. ?:98 2 2 26

0E84>498 (8419<7 07:4<4.,6 :<9.0== ,8/ ?8419<7 ;?,8>46 :<9.0==

/> / / ,/ + =/;?/8-/ 90 38./:/8./8> ?8309<7 <@ 9< +-2 38>/1/<

C 6/>

!6H C

$6 2

&: +8. "6H $'"%I!6IH&

./89>/= >2/ <312>-98>38?39?= ?8309<7 /7:3<3-+6 .3=><3,?>398 0?8->398 +8. ;?+8>36 0?8->398 90 ! />

6H )

C!6HH H ,/ >2/ ?8309<7 /7:3<3-+6 :<9-/== +8.

6H )

C"6HH H

>2/ ?8309<7 ;?+8>36/ 0?8->398

(25)

'DI: I=6I I=: EGD8:HH,6H 6H6H>H D;I:C 86AA:9 I=: 6=69JG$>:;:G EGD8:HH

0E84>498 )0<@,,> :<9.0== >2/ :<9-/== 90 (/<@++> 9< 38>/1<+>/.

+2+.?<3/0/< :<9-/== 3= ./E8/ += 09669A 06I

& ;

6H 6H9H I

-=: ;DAADL>C< I=:DG:B 9:H8>7:H I=: A>B>I>C< 9>HIG>7JI>DC D; I=: /:GK66I EGD8:HH '309<07 9< I A/ 2+@/

C06I. ; += C A2/</ ; ./89>/ + <9A83+8 ,<3.1/ 98

&?7= 91 44/ <@F=

0E84>498 /> 2 2 26 + =/;?/8-/ 90 33. <@G= A3>2 -97798 -.0 9< +8 38>/1/< C ./E8/ >2/ :+<>3+6 =?7 ,C

-6

$6 2

22 +8. >2/ -9<</=:98.381 +<3>27/>3- 7/+8 26 ,C 26 -6C 3= >2/8 -+66/. =+7:6/ 7/+8 9< /7:3<3-+6 7/+8

*! ,8/ &! '309<07=

'309<07 *! ,8/ &! 0 2 2 26 3= + =+7:6/ 90 + <@G=

2 A3>2 -.0 +8. 7/+8 2 >2/8

26 " += C 26+: += C

EEAN>C< I=: &! DC 6M N>:A9H I=: ;DAADL>C< G:HJAI

(26)

9<966,<C

6M+: M += C 09< /@/<C M

'309<07 64@0859,8>0664

-JE>' 6M M'+: += C

08><,6 474> '309<07

'309<07 ' 0 2 2 26 3= + =/;?/8-/ 90 33. <@G= A3>2 7/+8 +8. E83>/ @+<3+8-/ >2/8

)C

26

. += C

'DI: I=6I 6 C:8:HH6GN 8DC9>I>DC ;DG I=: %- >H I=6I I=: K6G>6C8: 7: QC>I: -=6I

>H >; I=: QC>I: K6G>6C8: 6HHJBEI>DC >H 9GDEE:9 I=: A>B>I 9>HIG>7JI>DC >C -=:DG:B >H CD ADC<:G CDGB6A "C I=: 86H: D; >CQC>I: K6G>6C8: I=:G: :M>HIH 6 G:HJAI

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6?.>?,>498 91 7,B47,

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&$'%2 2 26&& -%22 26&

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H=6AA H:: L=6I EDHH>7A: A>B>I 9>HIG>7JI>DCH 6G: EDHH>7A: ;DG '6 6H C I=:C JH: I=>H ;6B>AN 6H 6C 6EEGDM>B6I>DC ID I=: 9>HIG>7JI>DC D; '6 ;DG QC>I: 7JI A6G<: C

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