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Финансовая математика. Пыжев И.С. - 4 стр.

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ВУЗ:

СФУ | Красноярск

Составители:

Пыжев И.С.

Рубрика:

Математика

7

NbgZgkh\Zywd\b\Ze_glghklvWd\b\Ze_glghklvijhkluobkeh`guo

ijhp_glguoklZ\hd

 Ihgylb_ ihlhdZ ieZl_`_c _]h hkgh\gu_ iZjZf_lju Hp_gdZ gZjZ

-

s_gghckmffubkh\j_f_gghcklhbfhklbihlhdZieZl_`_c\h[s_f\b^_

DeZkkbnbdZpbyihlhdh\ieZl_`_c\hh[s_bnbgZgkh\uoj_gl\qZ

-

klghklb

Nhjfbjh\Zgb_gZjZs_gghckmffubhij_^_e_gb_\_ebqbguieZl_

-

`Zihklhygghcj_gluihklgmf_jZg^hijb

1

;1 == mp

.

Nhjfbjh\Zgb_gZjZs_gghckmffubhij_^_e_gb_\_ebqbguieZl_

-

`Zihklhygghcj_gluihklgmf_jZg^hijb

1

;1 >= mp

.

Nhjfbjh\Zgb_gZjZs_gghckmffubhij_^_e_gb_\_ebqbguieZl_

-

`Zihklhygghcj_gluihklgmf_jZg^hijb

∞→= mp ;1

.

Nhjfbjh\Zgb_gZjZs_gghckmffubhij_^_e_gb_\_ebqbguieZl_

-

`Zihklhygghcj_gluihklgmf_jZg^hijb

1

;1

=>

mp

.

Nhjfbjh\Zgb_gZjZs_gghckmffubhij_^_e_gb_\_ebqbguieZl_

-

`Zihklhygghcj_gluihklgmf_jZg^hijb

p

mp

=>

;1

.

Nhjfbjh\Zgb_gZjZs_gghckmffubhij_^_e_gb_\_ebqbguieZl_

-

`Zihklhygghcj_gluihklgmf_jZg^hijb

p

mmp

≠>>

;1;1

.

Nhjfbjh\Zgb_gZjZs_gghckmffubhij_^_e_gb_\_ebqbguieZl_

-

`Zihklhygghcj_gluihklgmf_jZg^hijb

∞→> mp ;1

.

 Nhjfbjh\Zgb_ kh\j_f_gghc klhbfhklb b hij_^_e_gb_ \_ebqbgu

ieZl_`Zihklhygghcj_gluihklgmf_jZg^hijb

1

;1 == mp

.

 Nhjfbjh\Zgb_ kh\j_f_gghc klhbfhklb b hij_^_e_gb_ \_ebqbgu

ieZl_`Zihklhygghcj_gluihklgmf_jZg^hijb

1

;1 >= mp

.

 Nhjfbjh\Zgb_ kh\j_f_gghc klhbfhklb b hij_^_e_gb_ \_ebqbgu

ieZl_`Zihklhygghcj_gluihklgmf_jZg^hijb

∞→=

mp ;1

.

 Nhjfbjh\Zgb_ kh\j_f_gghc klhbfhklb b hij_^_e_gb_ \_ebqbgu

ieZl_`Zihklhygghcj_gluihklgmf_jZg^hijb

1

;1

=>

mp

.

 Nhjfbjh\Zgb_ kh\j_f_gghc klhbfhklb b hij_^_e_gb_ \_ebqbgu

ieZl_`Zihklhygghcj_gluihklgmf_jZg^hijb

p

mp => ;1

.

 Nhjfbjh\Zgb_ kh\j_f_gghc klhbfhklb b hij_^_e_gb_ \_ebqbgu

ieZl_`Zihklhygghcj_gluihklgmf_jZg^hijb

p

mmp ≠>> ;1;1

.

 Nhjfbjh\Zgb_ kh\j_f_gghc klhbfhklb b hij_^_e_gb_ \_ebqbgu

ieZl_`Zihklhygghcj_gluihklgmf_jZg^hijb

∞→> mp ;1

.

 JZkq_l kjhdZ ihklhygghc j_glu ihklgmf_jZg^h ba gZjZs_gghc

kmffubkh\j_f_gghcklhbfhklbijb

1

;1 ≥= mp

.

 JZkq_l kjhdZ ihklhygghc j_glu ihklgmf_jZg^h ba gZjZs_gghc

kmffubkh\j_f_gghcklhbfhklbijb

p

mmp

≠>>

;1;1

.

 JZkq_l kjhdZ ihklhygghc j_glu ihklgmf_jZg^h ba gZjZs_gghc

kmffubkh\j_f_gghcklhbfhklbijb

∞→≥

mp ;1

.

Hp_gdZklhbfhklguooZjZdl_jbklbdbiZjZf_ljh\ihklhygghcj_g

-

luij_gmf_jZg^hbihklhygghcj_gluk\uieZlZfb\k_j_^bg_i_jbh^Z

8

 Nhjfbjh\Zgb_ klhbfhklguo oZjZdl_jbklbd hleh`_gguo b \_qguo

j_gl

Nhjfbjh\Zgb_kh\j_f_gghcklhbfhklbbgZjZs_gghckmffui_j_

-

f_gghcj_glukihklhyggufZ[khexlgufijbjhklhfieZl_`_cihklgmf_jZg

-

^hijb

1

;1 == mp

.

Nhjfbjh\Zgb_kh\j_f_gghcklhbfhklbbgZjZs_gghckmffui_j_

-

f_gghcj_glukihklhyggufZ[khexlgufijbjhklhfieZl_`_cihklgmf_jZg

-

^hijb

1

;1 => mp

.

Nhjfbjh\Zgb_kh\j_f_gghcklhbfhklbbgZjZs_gghckmffui_j_

-

f_gghcj_glukihklhyggufZ[khexlgufijbjhklhfieZl_`_cihklgmf_jZg

-

^hijb

p

mmp

≠>>

;1;1

.

 Hij_^_e_gb_ \_ebqbgu ieZl_`Z b jZaf_jZ Z[khexlgh]h ijbjhklZ

i_j_f_gghc j_glu k ihklhygguf Z[khexlguf ijbjhklhf ieZl_`_c ihklgm

-

f_jZg^hijb

p

mmp

≠>>

;1;1

.

Nhjfbjh\Zgb_kh\j_f_gghcklhbfhklbbgZjZs_gghckmffui_j_

-

f_gghcj_glukihklhyggufhlghkbl_evgufijbjhklhfieZl_`_cihklgmf_

-

jZg^hijb

1

;1

==

mp

.

Nhjfbjh\Zgb_kh\j_f_gghcklhbfhklbbgZjZs_gghckmffui_j_

-

f_gghcj_glukihklhyggufhlghkbl_evgufijbjhklhfieZl_`_cihklgmf_

-

jZg^hijb

1

;1

=>

mp

.

Nhjfbjh\Zgb_kh\j_f_gghcklhbfhklbbgZjZs_gghckmffui_j_

-

f_gghcj_glukihklhyggufhlghkbl_evgufijbjhklhfieZl_`_cihklgmf_

-

jZg^hijb

p

mmp

≠>>

;1;1

.

V

MQ?;GHF?LH>BQ?KDH?H;?KI?Q?GB?DMJK:

Hkgh\gZyebl_jZlmjZ

Q_lujdbg ?FNbgZgkh\ZyfZl_fZlbdZMq_[gbd±F >_eh

±k

 NbgZgkh\Zy fZl_fZlbdZ F_lh^ mdZaZgby ^ey klm^_glh\ ^g_\gh]h

hl^_e_gbywdhghfnZdllZDjZkghyj]hkmglKhklBKIu`_\<IAm-

_\DjZkghyjkd±k

 Nhfbg =I NbgZgkh\Zy fZl_fZlbdZ  ijbf_jh\ b aZ^Zq Mq_[.

ihkh[b_±F=ghfIj_kk±k

>hihegbl_evgZyebl_jZlmjZ

1. ;ZrZjbg =I GZqZeZ nbgZgkh\hc fZl_fZlbdb F BGNJ:±F

±k

2. ;mo\Zeh\:<;mo\Zeh\Z<<B^_evkhg:<NbgZgkh\u_\uqbke_-

gby ^ey ijhn_kkbhgZeh\Ih^ h[s. j_^ :< ;mo\Zeh\Z ± KI[ ;O<

I_l_j[mj]±kbe

 <Zs_gdh L< FZl_fZlbdZ nbgZgkh\h]h f_g_^`f_glZ ± F I_j-

ki_dlb\Z±k

<_[_jFDhff_jq_kdb_jZkq_luhl:^hYNhjfmeuijbf_jujZk-

q_lh\bijZdlbq_kdb_kh\_luI_jkg_f±F >_ehbK_j\bk±k

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