17
) n-t.LQC'l-1.0t'·~1( Q(lC( /;J_UY;;r2\.!CC~ -&/c:~ i ~ ~-- (mecv,- d'~u:~t'G'?) 1~(lrijrLl ~----_. ~. 9(ld. I.eV(co },=o] ~~~/f4,5"1 L t.... () .-;- .P ~tJ?/n3 3L<'I'f'''-' ""it) up -to no vv. Bw,;n~ p<.Qjed ( ~in<j'&<;:t.) - j Luit: pu-tt.in2J ;none.(:l ad a..- ~~ o..ccouni ( iJ.s<Y-.€.- &v.,(? ~r4Cn). Bd now tf,e. ~'" /:n.c{f(,,'M. o.=LU7?~ i.f;a:L t.f:-e. ,nt~ La.i.e.. f2t~~ c:..hOJroo ,,-1,,' "'/-:- .'.' ( -- - (J'~ '-0 ~ L" -1- A L I.,., it ~~ t= <=nsy{;U<..u; Cl.. 6l.V>tn~ p<-cri€Jd: '" ~J{ WCUj tf!.;a.L o [PV( L'" )=01 §V(ioTllL) ~ 01) C>~.~ vno--U:. I Ancs vI/en-: ~.~,

n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

  • Upload
    others

  • View
    1

  • Download
    0

Embed Size (px)

Citation preview

Page 1: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

)n-t.LQC'l-1.0t'·~1( Q(lC( /;J_UY;;r2\.!CC~-&/c:~i ~~-- (mecv,- d'~u:~t'G'?)

1~(lrijrLl~----_. ~.

9(ld. I.eV(co },=o] ~~~/f4,5"1L

t....()

.-;-.P

~tJ?/n3 3L<'I'f'''-' ""it) up -to no vv.

Bw,;n~ p<.Qjed ( ~in<j'&<;:t.) - j Luit: pu-tt.in2J ;none.(:l ad a..­~~ o..ccouni ( iJ.s<Y-.€.- &v.,(? ~r4Cn).

Bd now tf,e. ~'" /:n.c{f(,,'M. o.=LU7?~ i.f;a:L t.f:-e. ,nt~

La.i.e.. f2t~~ c:..hOJroo ,,-1,,' "'/-:- .'.' (-- - (J'~ '-0 ~ L" -1- A L

I.,., it ~~ t= <=nsy{;U<..u; Cl.. 6l.V>tn~ p<-cri€Jd: '"~J{ WCUj tf!.;a.L

o [PV( L'" )=01 §V(ioTllL) ~ 01) C>~.~ vno--U:.I

Ancs vI/en-: ~.~,

Page 2: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

no../ve.. c..en4LUc- ic6Jn

!~v ( L ) .P - L ( It G. _)_ 0} )p.V J1

p

---

/eA'£. .. ;oeL PV~G).---- --

-

IPV< i.~) ~ pV '( :) ~ 0 j) ) p V n( i0) > OJTr;en

L lpv~i.o_1-.ll~)_~~~V ;,(~o)~ il ;,oJo.n.J. ;'1Y7mUJI t' ~~;'CJ rL ~ 0 e.el ~ !

- im pe~ ~ t.o cU2J::l.f/'?:,e~ iD>In,3 j <.<.JYt ~evv1f12jY.'0.. c.C<9-UJC i. .'

- mcTLl2- a:J~~ecJ. p-z-o,je.u-& ~ 2i2.!:'r'r'~dC (incut?ln(J I >~J)o.rmui'-b/ ~; ~~ ~Xo.YY1r&--- €x:~/)d ~ l;v; eL e?e- CLY7 "$-1deruLcA

er.d€.5L )

- ,~ E. Eel -6 .J / I () ) . I-~ '0 '3L.U.d(1 ~E-._C!le:vva.;c/'v~

/ -it- J? V~ i )} W7d.

Page 3: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

'-"> l t.L~ :DCL) ~ t"lCan ~ i.fJ;<:S{,Cfl-ui. ~ OJ( evv~~t/nre~ wf!JeJL iBe /nv-e:;J;meYit-­

i"" p~ &Jk. (G::>rnp~ wi tfZ .tf>e ilme. OJ! R~ ).

B~ J rn~ 'I) (/"0--.:t£<f1. -t i,", --I:J5e.. fa eeo IN' rrdLe.rnrnCL-):ZPV (i) =- C I+L)"- DU) . Pvc i) I---- ",> ----.J

P2.oof?: iD - . . ~1 A . .-'4\ + fcsv--naE. dtffeJLQf) tftJA)rj~V(L)= L... K. (JTl..)~

and-.. --I:.10e de-P of J) (i) • 0,~ rneo.r-, cJu.n..cd::.iot( "3~OW -S ~o-vv ~f2r}~/ 6./ ve -t17e fY2..£Y.i e.eL:. -1::0

1:Ae. c.iLon ~ of Int e~ '"La.:t:.e.... ;

Page 4: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

]6. P v (La) =-,(;;7.05"- :DeLo ') pvc iD) Cl i QV

§ ffieeu<- cAu...ru:xJ6;'on ·fZ'L CL RC"0't.fc C'O of ~'(/~r~?-J3<.\~d:3

A~ ihcUC We. ~cuve. nc-t CA- SJ./n~ (§~n~ ~~ecJt;

&ut CL Rcsvt·f!ce6 o-f! .N - et· ffeR.Q-ni:: ~~~ pzoied~vvl'tfL nd ~f~~

l~A:~ tke)K::] , Je = !".,~_N ImCU'n eXcuY?r&~: A fXS?--i,!b~eo l-v/t~ .N, f3CJ/7ci8 0·12

~ A j /;\/2... goncl3 of i.gr-e IJ" L) " ~ .( \lV1' eJZ.. ~ cor; SS./(j€fl.fLct BeLo1JL/ I'r-c rncruz~~i &)

TfJen- )~e&~ .'_ . IV' _ --,--~.v; ~1Pr-+ : = PV"""'t = :Z;I?Ve (i) :=- ?;I?e-. IF<A.... r - (2.:. ( \

-~----- - - - PV3 o,f-Qv€/C.J-p'c-ojeG&INhcvt cJ7:xs~J- tXe- oI~/on?

Lemma.: I ~ ~e. . J? e. -jS)Pt,~ (L)::=' e",,/ DJ:: pcn::t:'.-- -- -~- --

M-oof ;-;------- -- - --------__ 0 n " e- -o4c'L ~o.n.~

~iL PVpod:- (L)=- O'L)"- :IJ[='t·P)/p=£-~~ --

\:= 4- (21 PVe) =- z: ~ P~/e. ~- (}tL5~ Zl J)e' Pe.:~ dL c.. cfc - /, 0'-----------------_ ..-) ~e :=:;~i~D )l ~:=: :LJ

2W'Y? ~.[2 J) UJ2£:L:tJ D /} ~ g:> e.. l/1

Asa/n ~ )' ,v, ~JJpo77t =; E ~I'=? JJ~-t ;~ CL ~Lf::.-IDl~·t.ec(

\IV; tf2c p:::sv' 6;v e- coef!ll/c.IR.n t~

, S> )' ~,_m~rL 'e... .:S ~~ .:5 mr-Ve2--~ Gl5';,('. f~L PG0~ d

~I

Page 5: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

IpV(i.o)=O~ fjf-EVCio)=O]

[~PV(io) >o.l

TPte r:xn-t.foeo I€ /rnrrJ£LI7;i:,ecA

TReo7.!Uf1 :

i,e.

· . . 0 crd .fc:-0'~L edlJ.J2..l4: I(Y1m l.AJ{J :z:.a-kI01( ,0, P._

A~e : .1) We. ~GUv'€.. <VC.. ogeSa..i/o,? e-f L pound-3­

w ~.~ /~ du.e.- /rL T- ~eQ..Q.~.

2.) TBe "-~-t ird~ =Le. /" Q and we..

~ Siver>.- p- pou,r,cis now (a;;{; t.=o) vvit ~

rE ~ L ( i-fio)'7']

3) We inved:; me.=2..- P po<..<r<J..." ,-n-to N" ~n~

P'-cfJed ~ (w/fJz,__ net C-=;F{f&1N"3 -- (A"e, -t. ~ ),c:: , eel" IV )

'ULch -I:.J'?Cx~ ~ ~ffbvvs. A~:::-o ""-e- IlOQ-Qe8~'I) Lei iAe;:ne.=.nt v~ 4' e-~ P<=jed

a± inte=d ~e.- Q &- Pe.. fr.r?cJ.it's rYJe"'-hof w<...a..:t./CJr( ~ 'n~e. .

:De.f? 4 p=-t-fl"e/oa of N ~",><n~ P20jec;t", Is irr,f??<-u-,i'aeelwlt/t ~ to ot?e.8o.L~ L d'"-€.-.cb in.- I ~cvv,cd:. ir,-t~ ~e.- @_ l-f cl/?e.. p~t ~ ef2ifJe. w6& '"2C>;jed-

jPVCi.) = F l?t;,;CZ)- UI+iS:J?ev:, CL &c~ m//) i r>7 LM'rI ak i~i.0 ev-.ci -tJ,; 5 "7/17/"'_ i, o.

Pz.oo·¥ :

o -=- I? V (l.o") :=.

Page 6: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

Le't~V(L") = ~'Ak U+i.)+'1<. - UHi. 5T)..

we. 'L.f<>-nwn e7-cU1:...e o..JLL A K,e:.. (:"4'(0<. 1:::.. :; @~ Q. ~./n~ i'rJ de >< ~.

(foC-. 'Si.rnper·c.../~)

~-(-L-) -=-=T __L(I+L~ ~'{;: (J+L5+.K~~

in. po..J7.-t./C(Ae.CJ.SL ) -(!SL i.:. i <.:>

~ !L p V ( L0)---.-, -L (1+i.D")-T- f' f1k tK ( / t 1.0) i" }--------------------- ~~--- ------,-----

Page 7: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

c.on.. v·e X

F/n~ !A»Gn3 L~a..:t Dpm:t. = T

( irLo)2- i~L:J V ( La ) ~ p L 1)p:t - T 2 J ::::0f<fl-ta.-~·t~ ; ~ p~'(Jt'e­"n oJLL oth€JL c..~

Or7~ ;"·f -t. K :. T (-t.uV,·d

-tJ!Je... ':neCjMcJt- t(j i g S·t ?../c.t.. ,minimum , o

E~~oi:/on2-.

IT~ 2-,-_1)'+;,+£'""JJ"" 0- much. rn~ in~d:~.togeJd,or? -Lm-€- T --

~f2Jotdd &e CL W-€./~ rY?~ o-f? £J~/6n?::. D, H __ JJ,v

.~ oJ:.. ~ one of J)e m~ Be .~~ i~cur. -T !~ (UnCS2.-, f{;e. me~ oiwz.c:;.;lfOr( /-'S aAo CL vve/gf-vtecA 117~!-/2"~

of tfle t?an3aub'on 6rm~ t~) o.:t e~ one. Gf.

{fJe t.w...n'SQcL6n f/rne m~ rk. ~ -l::.hCLrL T-=> We. '3 f{ ou.fc{ f5e aii& .-to g eP..L CL ?-""m /'1<3

l ac:bve, non - !"n;~ed) P=,j ea in od~ to f'«l the o~8o:&"on!I-Iow can. we ~ {he nort- f!JC0'VVvYlecJ[ ~/:.o.;I;;o ?

9to~ mOJ2 Jbd: "ss ne.eoIecA. . ( /l..0{u,r<..eY» ~l7d ~ ~ e-be.. )+ ·t'nOJJcia-i- J€S7-ivcx..;{; v~ "

Page 8: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

· i den.. e

F?.om i~~i'~t'on ·t~E(j~ : we need to Be o.ir&.. to ~Q ULnr/l'/('8 ~ p'wjed.

#<9W'G<..oI'\jg (Bef..,~ e.""",~7) OJL '/]V~ ~~ Q eat cf

fino..n ua.2.. -1:.= e-s to 6'21) Be£€.. 0 ~ 'il F;",,'2R- Q non _.f,,.,"BR eat(even. not gto.n..-'teo( s-d) &w;.n~ fJ?.ojed.

Page 9: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

We.. wl ee.. CLJn",iciv<- on~ "~e" g"nd~ w;t./4 Seqo v:J,.;(QJ'1cA Jo !to·t cen~;cleJ'L oY2~ V'~~-3 ~),

Il?CLLC\\-cc AE!.iZ.- 12_ / 'tf) D, I_____ ' OW<- CJ0I7d ~ Cl.Q..e WI·I<- 1" >(ec{ C.O~

.z..cJ:.~ (f &x:d.l'n8 c.o~~ zcde~ QJ?!Z.. ~d ofe.o n (,:y/cJ.eR.cJ.-ij or;\ ,

o.il... ~fYlerd:.-s. vJa;ted. IN,i~ -Is!=. ~

Cl',-,,-f/xecJ ~ €5ond. I'~,

Tf4e. CW1.fU2}1t f?-'2,/~ of &n~, e(j mc~~~.

j-4cvV ?

T I?e CUJU'?.Q.n t ~-te... 0f O{...U"L. ,.'ale f) ¥"V">/", n ··t I ·i ,I__ ~--'= '._' '\..-U_~__ I ':') of€. e'?fn(P'7ed\

&4 on e. PCA.l<..ot.rn . t.eJL. (f . 'L l!J t u(o _.. - e. . . f. ?-E::.... '3-U'7?~L rJ"bC €:':X.- ) _. C~\)"lk.f1 . ~ I~

'TR/~ po.f>-..arneieJL. c1t~ CUY2c.6nt'(.o~ ') ;'n £1' rn e )P-,UT I~ f,.?j~] on. &nJ-s CJJLe... corn~ec1. h-orr-,

t.Re. ~J?:..{;/Ot0

l~·C-l,()-'f.J2..J<:..n-' --t.-I-.I-R---=.-C-u.tlR..Qf(-~ T ~.,,-€d],1rt c 'f=g E:,)"L \;VC5l..-ci'3, t.f!J e CLLQJ2.QJ7 -t p'zk::JL ""3. ·f~cJ 0--".> ~

lE__ PV of~ ~,n;n~ ~i'S w7tA~~~J'c~1

"""> A n(j feuciuo.1/~"- ef f. f?> <?_ Cw1f?JZrd:. W' e eel. i rnl"YJ eci 'o...&lz1

ePun~ JL &nd. p'z./CQ.5':,.1

of ~ +fi.'s:, modaL cieJ;.CfYk,." CL .,ia.A:ic. (dectd.) m~~ce.. tfie inv0SteJ'V-, w=.. not mo-bv'o.:I.d -t.o ~ 6L ~!:fie_ Bond :s. Tfje.. p"""f2;-e of aLl... &,ne1g ; '3, .[}; €- ~ C\YYIe !"

/J 1/~ iI I ' a.Jsla n. I/3d /,t 9.iy~ 0.. UQ_,.'~t0n~;l~ ~~e:'Wc>"'2deJC.. O'fr~CJjJ 1/111 •If . j;{

1_ I!(J ID / . 0 () -I- .'=. not ~(.f'- to-'1.QLrnCGl€.V"n~ tne.. .!!::rnamJc2 aT 0.- rn~ ,-~ --6-

Page 10: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

o

;11 ,-

1 :~Mo±W>J t;j,',

17 =-¥ o.c.:..Q... . VGili~

~ ~_ m~ t.~ (nu.rn (5e,,<.... of ~ ;;vf!,iek the 15:o/,J eves)

• @,_ mvnikn- of p~efl-t«; (=c'/="-';» P-~ ~-

'" CS -~o.co- v~ (t.f?e OJY?-p1""-'.l7i: of moneJ f'U-1d Lo-l:.h l2- gVile?-<.... ce:L rn o.-t ~u-u''<:J -t;' rY?e.. '

• :])} OfYl=.nt of rnon'7\ r~ ~,,--fj Ct.Pn.=--EI-- rn.. C~~)o.¥ c/ fY1e.o.c~ . ','

~ If. fXl:'",-c.vY'e.:L€J?.5!:, d,,;.Cercf'YJ'neJ:l ~. 1::J?"e fbn-cA ,.~'C

+ J? - (JUCf2- ",fO',e- ~nc) (~ de:tef>Jy.,ind ~Me TnaR Ifdlj',~ -le.he cu.N>J2J'"? t moJ2. fl,.d. .!3(.e. U )

fC4-c....s.2-\/cJ:.Lu2~

C-&UjJ6>n'~ .

~r~= ~ ~m 1- nu.m geFL o~ Cdu..pa>n';5

. I~~ v:J:-e- = %l (u"u.a1o if' pcyc.cflnts. ). /')

peRLQ.ritaae- of thE:­lli7J3-L~'6fh.-

Page 11: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

- IV\

~ P - f-1 ( If-(\.)c.- -m

- 'V\1- (1+'0..)

(l+Z\,)'/ rn_ :i

m.?

I p = , 'p (1+ 2lj fV\ -t\

Bon of.. prz-l U2../i r)+ ~/?>e/ACQ.,t!jon -ss 1I

{\ (m~ .eec~ corn1:J<9~VJcje,lun) . m

Co. C\: ) . "-IT ;-n '= (It' C\. )

. _ - fV1. 1-(f-rCl)

()t(l)~m,_ :i..

fC'uY(idcL

Page 12: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

--=>

Finc~: ~CJx lIned /on / ury?peijZ·cccl::;'<...""J re .-

(,J<) { '21.. ' rn )~ R.] (we&1 CfY)vecdrff1i2.

~C)me.. z.€..GU.>en-3. efl-en rn- I g -the. '3,CVYI-E:. -/?se o_l./L17 17 ? / . I /' . 1/L€:<:' ...."-::>cnc......,e:,>c.e- &/?-o< 5 eye -U7E:.... rno..rY<:.Q:t: (n'?,:::: '2, j<;> c~ )

Met?.- (-,\J J~ cfx:ur~ Me d'!!:1 of {he '<r B eel1:..he Ino./1.j~t) gLUt nol- ~J;E:- f)'VC.rZ~~,

J. j-:=. .r ('",'-r ~)- T7.L1 c. (', , ((I. ,- n )'--1-.._ r ,,~ C\. \. /".- \../-1- m ) .

f!lCLLCL«-&?j '"<, dwdion '~urJ~"/vo\.l'\/) c-cn~dE.Jc-t.Ae. In ve:;;.t(St../'J S ~cl-e.~,.;;

p

,.-re

Page 13: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

TJ0-'~ q;v~/cn ~ ~

A &nci ;'s &.uslvt a:£ [:;; == 01 ~t p~/C-1L I~

~ -I Re... CW'ULQnt__:tie£o( o_£ffl E- rt'Jcw-rkd r ~ ct.Tcd le = Tj

@ WJ?d i '0> t~e. rn~ p-uc.tL of ifJe.. 807cld If =..rT!?

[e] TRe. tjono< /3 oflfleJCQci rd. jdU~ P.1. cd It. ~ T j

wJ?d is !fie. inVC2c¥£YL , 50 IYeU :f ile< 8"J" tt,"

Lc)} Tfte. ;'11 vevtc,- woni~ bo £efL_ i,£<?- fb-V7c/d p~v~ t?i cut /hrl, Whct:t /'?:. P7~4S.

ever;tlAG~ ~jei~.cj/f? f!tE ~ ;/:-?An~we~: 1'551"lcl PuJCk'-. ~o ?/YJv1cc.

I p =J

j::-

('" (\)Il +I, ,_rY1

C- (, I/I( J '- --';'- nt,- (h.~ )m )}9>-Lr-rcp er '~. co_l.Jor? " we.. vViet. c:...on «,..t'n e '- ~V7 t£f

~e Q~e Ir = ~ I ( ,=XQc;i:~ o..f£<:Q. £ fJ, e. e- !:IZ .

c:...OU{00t<.. p~ eR-t )~~ ~ . I

~e.rC.O.jL. c..~e- /3.3 6'aJ7..-[. <j m G"-e- ccrn/d,rCtUceo((lfeesi -to d.<s.cot.urt <:Y<.. ~r0;;JCJG~l/d( -bo{f?e. n eo.r'LQr"~';;&

P:::J1'nc e-~ T= tC./;..." ')

J (J,-,,~·f neecf. -i~,o "2J2I;;>,f\.'J..c:.sL. tL ~ n - C "~

&nd 1')'V~ kv?''Uc-e:''cl..- _

Prn=ibc (t) - (i~A )fJ-e + ~ (1 -- (-;~-~'re) )._~__ f'Y1 _ _ -

c~ec~ -~ -<!:he. ecr~:=? 01 voJ.~ fl~d .'

Page 14: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

&) 1nL K,i 8. <::'CL5J>l2..Lf5e::. P'?-/CQ.. Pi "8 ffnt9VV 0_ / ~

J 0 ' . /J ~ I ':\ 0 0 , e' J 0 . '{/Q<"U-ZcA .fL<:!Y77 -L'/z,e'7:.-ne ;y e Cc/\. ('- ::> heLl..O< BE'.- -re

@Ono( 1;r2..:~{b--..rr(A:.,,-eCL

f Pc:! = (;:~f-e- -t- .~ (i - (J., :;,5n",)_'-..:.....----------~

( f7e e.O< -1:.0 'Sc6/e -L~1'-3 QCfMo..l.. 1o",,? / )

l:> - Pi . C. [. ~ -1~ (1~ ~)e -r re 1- (j1-~)E __

( even t4 e e. 'it'e£d C\ ~ ~ ~c) <gcocZv,'2f-I::.X j'.~ ,e7/IA.~/C),( ,I )

in -two th.vt eXGfYJ/~, we. l7eec1. -to '3oC've.. i/';e.Q~~/'Ot( of H?€.- ,Ksu-Y(

t~l ~ I~ ~~co~~~Joften.. t.Ae... r5o....,c/ i';;>'lUZl<... f,x c..0'y-'<-vc ",,,-"e... .~ <-u...0J<Jlni &-/" (1o{on tAe. rI7~ and ~ sdi. iI7e rbnch" d A."!:!S

P > F -' oJ6c> ve pOv'L

:: ) P e:d!.oi/./ po.re ...I <-

w/l:~ 7.12->spedto ct.·0 A e~ 2I."/C. fJ0>J/701Y( 0f <:nde.JS

£ (1+1.'2 ~c.annot t5e_ '8.oeveo{ o..n~/t-{'C.~ .. ~

i> nWT>en.I<-~ ('Y"F '0 xlmde. ) ."!ofu-bac I", 17l2~c(J~

~ > """;173 Ne-cl/idn "s me~ci. eR. m'hV -ex.-d'-'j », JSJpee:.lc~fl7o,.nCt'o...L pG.~ct?ca~,

OR. -:Some. spec;0J2. t(~~ Q.l?cl 2Y!.¥. fJ,8

E I<¥/O'::' ·tAe... c."'-'1><2. wf,er'(. {Ae.. In,boJl p1.7CQ. P/;;:; ecpvlO._L tetP7e- lo..~ va..£il e.. (Me Bond /s::, ~a eC/(

CLt PG'~7....), 7-»erL /fLorY( C:Z-0r70[ P'UC(Lf/:su-nt-L~eCC /we. h</(/l/€'-

Page 15: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

- ---- ---------

\

\

\

\

:Oc;)/!' - --I ''0

C[WI.:lfj~ .- l/ruc e..-. ·fu.nd/on o..f-jtj, eee?( _ _---p(J..r>"D._rne·teJc_~: CQLt..p:cn 'Levt.-e.)

ma..1J.,'-.n-l·td (n. 0'2..... /Vl = .::r ')

CD" cJ... n tun ~ 0...f­c:.~~ T'rf.fcOJV'2~

n ----r-----' 0. \) I:= i_+ rn... C.O(YXJn Lc0CE:-. _) - c..neCA'C.-

Cl? = F ( / + JVl. ""''"I-=? -ude 51---'- ~ - -----..

C. CV7 .Be.. '~L-vtc;( 1-c.~ I'r; t:-eF2.3."e0l/c':J ((

..... Dj! ihe 'g1Z..a.pfl<- (IV;'t~ PtCJ? .../ &-~'?&.~erne' p - /009 .-/

- r: - 'O~-. _._.~ -,..... --- .- - '-.fou..nc/( f"Zo~' -~-L he -V~e->0~__'

(\ :=: 0 !2.C')n-r -L,/J; e /be. -mU((G....-

)~ -=- 1.+ M . c.c~ ?-o..;l~~

'vV e..

---- ... ~ ..- .--"

'.

r

I1 '--"--...

---~ I - ..._.------\ ----

fV\~~~L

o

Gnceu.>';~n: t.f7e.... /;)0-.0 ...•.•~ t­. '-'-'-'"'1e C'C.. :?::>

C~CJ~ ~ OJ?d C!2edt...uu l:.~ .c:o.n Be ~Q.,'>I'e~lb(.u'7 cl(

lj..cnc lAe ?P~ f{ ~vve /{l

jnollL72J 1'8. w-z./tt€J7 0-<-

exptct-ned. CT? t:he- cwuv~ ~

Pwut.~~ rY(- it v...J-rJ ~ o-f2C<!9-t~ peR ~().JS-" ~~ ~d.~ a:!. 'Ven .' ..'

( lJ.~U~ ,,-b / ~ ·f; xe.d., -!>d.~))

m=: 2. )6"2.... ''"2..{If =- ,..:)

Page 16: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

Le0t~ (e~-l ') Immun;7;;cJ::k~n-UJV;'Vd-t~

.modee IYLCJg~: AR. invdcC-. M~ cu< age~Cvk/on

1::-0 f~ L cd it:=: 'r) ~T;?;~ ~LU?-'li2Iit /n L~t Gcvt"e-( CWV'U2J7 t: I/}'J Ct.nJ=.12~f:.. ~iei!d) ;'S L CLI(O( I?e l 3. a" vc..rc..

fP= L Cit-L)-T!

No . ,', .) _.~. ..1 L ,., ')' 0.W \.t. ""'"C), ..J.n i.l2:".:QY;/L 'Zc.Lice rr.u~ vC~-(j '?Jif:J~vLcJj .

.A I'm :1::.0 CJ:Jn~ 2AA_C:7t Cl.. t6cc:''>f.(o e~~ jcn..cied- fm..- {Y>cd:.

, ,7 e, .I, '" d d P f/; \o C /S ('U:I DI~ ; IYtfY(LU ....// ~eoe -I:t.J <3/,,")c.cILC C/h()...j"-18~ 0 ') \'0 L~/pi

rr't/n J rn u.rrc cUt L =: L<::)

CcncL'6cY75~fOL Ihe..Coc:cd-.

f)'71 f)im t,t..-fvr

Pi/kkL (I:)' ~-) -PV:U ('0) = 0)PV~~tL ( io ) := 0 -/...._-----.-

1~~ =: P~u. (/~')"=

S);:.f ~~ b<:J;ln:J ~ i --PVJ. (L'e) +.-+ P VIv' (La) := A+ '. +- J:J/(,/

\ VLi~ (P~·t:-vd~ of .ec/?1~7ei7t:s

l.Dpcn:t ' Pf'6d = 1),.£> .'..~.DA/ . PA/CLYl 0 i:Ke:"'L i,YI ~0J7 1:; . 1fOu..-t(. ex.... - ,A Cl no-1=:.' ~t­

f£/g ~f /

Page 17: n-t.LQC'l-1.0t'·~1( Q(lC( ~-- (mecv,- d'~u:~t'G'?)personal.maths.surrey.ac.uk/S.Zelik/teach/Finance/... · '-">lt.L~:DCL) ~ t"l Can ~ i.fJ;

Ip=.1.U", ;:0.1 Gi~ ' ; p~ Ppo;-i T= 'j)p~ If ml?7un/ beet _ _ _ .J _~

5)rX';v-t / & Q. vver'f!fUecA. ~'Y? ~.f! eO t.: _

I~~,-~f).;j < J)p~-ut < rnclJX £ [)( 1-"dJM jl'L _ __ /1 . ,

'1' -;f' .-t.A~ ,.·nerrd/I:>e~ ,not -geub'4ecl /c--"L ", __ t'mmun/eo,.i/orr /~ ;'mr~\./t.--faf

T~:~Jca£e.Xc<..rnr:f-g... f!s..crn~Errt3. t::jf tJ7E- pc;;-uffo-f.:',o c<...~

(2:> 'nd3 0+ dr'Pfer?-Q.J7i ia1Ge...Cono,t'cieJL ~~Aec~ of 2- Gond~ Pt Ql<cA bw, tPc. b?.i~ 1'7'2 P :> I I <;'\ lAI . ~..,) . i Be.f7cAA 0Jl cJ..L.1. r50nale CIJ'1cA C4'Wl-cvt:J 017 s:, ..JJf!j <.).yX~..uf!:,

.l?-z.c;,ed A: A / Po.. (J n / /1o.J /v 4- c'CPl ~ '-11 l~ono1.;-1

J~cjl2-cJt 13, : /V~ c..cj?1 e--';) of l3o/)cl G

.TI~ '- - -I.Of/'t : Pi /J I /l . .J 0 /J I 0 . } IJ .L D' ,r~ DOnOl 1-1 o..not I' 2. ~c.n0(. ':J - m iA-'VC. (')e. L.. PI -e.....

mo:nJ~ /'&i_/~ of gone!.;q. o.ncA l:Sand 13 .'

(cc~te.J e<:J tf;e P:,<Y7cl /~/~ 1-~"1Jl>".k,)Then

:iJPIoJQc::.:t 11 =. 1)A

J.) PLojeet B :::.~ 8c.erJo/i ben -'S,. I t1/rnlN/11' '?;0--'-6{01l

pL :=:. P_fd:nL.. _

l)fX5i.L~ T