ASYMPTOTICS FOR GREEKS UNDER THE CONSTANT ELASTICITY OF VARIANCE MODEL. Oleg L. Kritski 1, Vladimir F. Zalmezh Tomsk Polytechnic University, Russia
|
|
|
- Roxanne Riley
- 6 years ago
- Views:
Transcription
1 AYMTOTI FOR GREE UNDER THE ONTANT ELATIITY OF VARIANE MODEL Olg L isi Vladii F Zalzh Tos olchnic Univsi Russia Absac This a is concnd wih h asoics fo Gs of Euoan-sl oions and h is-nual dnsi funcion calculad und h consan lasici of vaianc odl Foula obaind hl financial ngins o consuc a fc hdg wih nown bhaviou and o ic an oions on financial asss wods: EV odl Euoan oion Gs Gs asoics undling ass isnual dnsi funcion Inoducion Th couaion of aginal bhaviou of Gs o h sa divaivs of oion fai valus is ioan in financial is anagn Gs sn h snsiivi of h ic of divaiv scuiis wih sc o changs in h undling ass ics o so ajo aas li is-f ins a si ic volaili σ iaion i T i o aui τ o h infoaion abou bhaviou of Gs has acical and hoical ioanc sciall if anags us hdg hi scuiis fo ducing is whn fuu undling ic has no good assssn o sia h quali of h anagn of oion sag chosn Gs and hi asoics lo fo an diffn was such as fo ofi and loss aibuion and oic conac dsign and o caliba aas fo a ics Fo insanc i can b usd fo finding Blac-chols ilid vaianc bhaviou [ q 35 8]: wh T E F T E F T d is a G gaa fo Euoan-sl call oion wih ic σ is a osonding auho Tos olchnic Univsi 3 Lnin Av Tos 635 Russia Tl: Fa: E-ail addss: olgol@uu
2 F local volaili T cd valu is a filaion gnad b sandad Bownian oion W and E is an Th aginal bhaviou of Gs is also usful fo couing na-fuu ic sn ic fo Talo sis wh d a nown is a G dla fo call oion Fuho Blac-chols quaion [] givs us a laionshi bwn Gs and call oion ic wh is a G ha fo call oion foula [] o wih Lalac ason ansfos [] o wih invs Lalac ansfo [3] No onl h Gs asoics bu iing bhaviou of so oh divaivs of oion fai ics a wholso in financial ahaics This is u g fo h is-nual dnsi funcion T T fo final ic T ha agggas all aoia infoaion gading fncs of divaiv holds and undling ic dnaics As i is nown [] T T ooional o h scond divaiv of call oion ic T cis ic : T T T T is wih sc o h In his wo w calcula Gs asoics scion and cou is-nual dnsi funcion scion 3 fo Euoan oions und h consan lasici of vaianc in bif EV odl I is a ind of sochasic volaili odl fo h valu of undling ass oosd in [7] I as ino accoun h ngaiv colaion bwn soc uns and alizd soc volaili lvag ffc and h ngaiv colaion bwn h si ic and h ilid volaili [] whil h classical Blac chols odl [] dosn Moov h is so vidnc [9] ha is-nual Euoan call ics can b non-onoonic funcions of h i o aui τ in which incasing i iniiall incass h call s ic bu af so oin sas o dss h valu of his call and hnc is ic can subsaniall diff fo sandad suls of Blac- chols Bcaus of is ioanc h a los of financial alicaions of h EV odl in a wid vai of cons: icing Aican-sl oions wih nsion of Baon-Adsi and Whal T
3 asoic ansions of oion ics [6] saic hdg of Aican oions [6] and Aicansl noc-in oions on dfaulabl socs [5] binoial aoach [9] odling nonlina ulivaia ins a ocsss basd on i-vaing coulas and EV aoach [5] and an ohs Asoics fo Gs und h EV odl F Und h obabili asu of obabili sac Ω F wih a filaion T gnad b sandad Bownian oion W=W h EV ocss assus ha h ass ic {= T} is dscibd b h following sochasic diffnial quaion [7]: d d dw wh = is nown μ is an cd un a δ is a volaili and <β< is a scal cofficin o lasici of volaili ha as h local volaili ass ic gows dclin whn h No ha cas β= cosonds o Blac chols odl cas β= is h absolu diffusion ocss and cas β= is h squa-oo diffusion odl boh of h a dscibd in [8] L fo now on T and wih cis ic and iaion i T is ssd [7] as wh Th EV call oion ic is a colna non-cnal χ -disibuion funcion wih ν dgs of fdo and non-cnal aa I a b snd [7] as wh gn u n n gaa funcion G n gn d G n u I u du gn Gn n is a dnsi of colna gaa disibuion funcion n is a is a colna gaa disibuion funcion q z and z funcion of h fis ind of od q I q z j j! q j Th EV u oion ic is as o find fo call-u ai [] as follows j is h odifid Bssl 3
4 3 losd-fo soluions fo couing Gs of Euoan-sl oions und h EV odl a win in []: a b a Vga Vga wh I 6b 7 8a 8b ω> is a colna non-cnal χ dnsi funcion L us ain h aginal bhaviou of Euoan-sl call and u oion ics and hi Gs in qs 3 8b whn T as a Fo q i is obvious ha In addiion Fo aing h is ndd w should discov h asoics fo all h funcions ingoing o ssions 3 8b u I u du u =sub u=z =
5 z z I z dz 9 u u I u du =sub u=z = z z I z dz Fuh w us h odifid Bssl funcion asoics whn is agun z givn b [ q 97]: as i is I z z z o af subsiuing ino 9 and coling h squa disibuion funcions a win as z z dz =sub z = d d O = z z dz =sub Fo q 3 w obain z = d d O d O 3 Using q w can discov all h asoics of dnsi disibuion funcions ingoing o a 8b whn : a E 6 E b c d 5
6 wh and a consans ha indndn fo τ Taing h is in 3 8b and using q and asoics d w g E E 3 E E Vga Vga E Bcaus of h fininss of h i w g as b E Fo q i is obvious ha Fo dfiniion of EV odl i follows ha < i as 6
7 Li in h cas w find h asoic bhaviou of disibuion funcions ingoing o 3 6a whn W us qs 9 and h odifid Bssl funcion asoics whn is agun z as i is givn b [ q 967] Thn z I z 5 z z dz =sub z z z dz = sub z = = d 6 d 7 Using 5 w discov h asoics of dnsi disibuion funcions ingoing o a 8b whn : 3 6 8a 8b 8c 8d Taing h is in 3 8b and using asoics 6 8d w g d d d d d 3 7
8 8 3 d d Vga Vga d d as c Fo q i is obvious ha cons cons Thfo w us qs 3 as disibuion funcion asoics and q as h odifid Bssl funcion asoics W hav 9a 6 9b 9c 9d Taing h is in 3 8b and using asoics 3 9a 9d w g d d =
9 9 d as d whn d d d 6 3 d = as d whn d Vga Vga = d
10 as d whn d as d Fo q i is obvious ha In addiion Thfo w hav h sa asoics as in qs 7 8a 8d o w g d d d d d 3 3 d d Vga Vga
11 d as T d Fo q i is obvious ha T T T and wh is so consan ha indndn fo T In addiion Taing h is in qs 9 w g z z I z dz =sub T T z I d z z z I zdz z dz =sub quals o d z = d cons No ha ingal in q is a Lalac ansfo fo h funcion f I as i is givn b [3 q 8 97] On h whol Fo dnsi disibuion funcions w hav h sa asoics as in qs 8a 8d so aing h i T in 3 8b and using qs addiionall w hav T T T T T T T T T T I T T T T T T 3 T T 3
12 T T T T T T T Vga T T Vga T T T T T T 3 Ris-nual dnsi funcion und h EV odl nowldg abou h dnaics of h is-nual dnsi is ncssa fo h icing of an oions on financial asss [ q 3] vn oic and col [8] Tho : und h EV odl h iss a is-nual dnsi funcion T Euoan-sl oions wih h final ic T = wh oof: T T T T To cou T T qs Aa Ab Aa Ab]: T fo w nd us h following auilia laions as i is givn b [ Using q w a abl o cou h following aial divaivs: 3
13 bcaus follows: o diffniaing q w hav inc w us q 3 fo couing h scond aial divaiv as Finall ducing siila s and silifing w g This cols h oof Acnowldgn Th wo is caid ou a Tos olchnic Univsi wihin h fawo of Tos olchnic Univsi oiivnss Enhancn oga gan Rfncs [] Abaowiz M and gun IA Handboo of Mahaical Funcions h d 97 Dov: Nw Yo [] Ballsa LV and c L icing Aican oions und h consan lasici of vaianc odl: An nsion of h hod b Baon-Adsi and Whal Financ Rs Ls [3] Baan H Tabl of Ingal Tansfos Vol I 95 McGaw-Hill Boo oan: Nw Yo 3
14 [] Bdn DT and Liznbg RH ics of sa-coningn clais ilici in oion ics J Bus [5] Bu R Gi L Hadi and Lubano M Modling Mulivaia Ins Ras Using Ti- Vaing oulas and Rducibl Nonlina ochasic Diffnial Equaions J Financ Econo [6] hung -L and hih -T aic hdging and icing Aican oions J Ban Financ [7] o J Th onsan Elasici of Vaianc Oion icing Modl J of ofolio Manag [8] o J and Ross A Th valuaion of oions fo alnaiv sochasic ocsss J Financ Econ [9] uz A and Dias J Th Binoial EV Modl and h Gs J Fu Ms [] Dnnis and Mahw Ris-nual swnss: vidnc fo soc oions J Financ uan Anal [] Gahal J Volaili ufac: A aciion's Guid 6 John Wil & ons: Hobon NJ [] Hull J Oions Fuus and Oh Divaivs 7h d 8 nic Hall: U addl Riv NJ [3] Jo Yang M and i G On convgnc of Lalac invsion fo h Aican u oion und h EV odl J ou Al Mah [] Laguinho M Dias J and Bauann A On h couaion of oion ics and Gs und h EV Modl uan Financ [5] Nuns J Ruas J and Dias J icing and saic hdging of Aican-sl noc-in oions on dfaulabl socs J Ban Financ [6] a -H and i J-H Asoic oion icing und h EV diffusion J Mah Anal Al [7] chod M ouing h consan lasici of vaianc oion icing foula J Financ [8] sana D Maazzina D and Fusai G icing oic divaivs loiing sucu Euo J O Rs [9] Vsan D On h ulilici of oion ics und EV wih osiiv lasici of vaianc Rv Div Rs 7 3 [] Wong HY and Zhao J Valuing Aican oions und h EV odl b Lalac ason ansfos O Rs Ls
European and American options with a single payment of dividends. (About formula Roll, Geske & Whaley) Mark Ioffe. Abstract
866 Uni Naions Plaza i 566 Nw Yo NY 7 Phon: + 3 355 Fa: + 4 668 info@gach.com www.gach.com Eoan an Amican oions wih a singl amn of ivins Abo fomla Roll Gs & Whal Ma Ioff Absac Th aicl ovis a ivaion of
Derivative Securities: Lecture 4 Introduction to option pricing
Divaiv cuiis: Lcu 4 Inoducion o oion icing oucs: J. Hull 7 h diion Avllanda and Launc () Yahoo!Financ & assod wbsis Oion Picing In vious lcus w covd owad icing and h imoanc o cos-o cay W also covd Pu-all
How to represent a joint, or a marginal distribution?
School o Cou Scinc obabilisic Gahical ols Aoia Innc on Calo hos ic ing Lcu 8 Novb 9 2009 Raing ic ing @ CU 2005-2009 How o sn a join o a aginal isibuion? Clos-o snaion.g. Sal-bas snaion ic ing @ CU 2005-2009
Lecture 2: Bayesian inference - Discrete probability models
cu : Baysian infnc - Disc obabiliy modls Many hings abou Baysian infnc fo disc obabiliy modls a simila o fqunis infnc Disc obabiliy modls: Binomial samling Samling a fix numb of ials fom a Bnoulli ocss
Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors
Boc/DiPrima 9 h d, Ch.: Linar Equaions; Mhod of Ingraing Facors Elmnar Diffrnial Equaions and Boundar Valu Problms, 9 h diion, b William E. Boc and Richard C. DiPrima, 009 b John Wil & Sons, Inc. A linar
( ) ( ) ( ) 0. dt dt dt ME203 PROBLEM SET #6. 1. Text Section 4.5
ME PROBLEM SET #6 T Sion 45 d w 6 dw 4 5 w d d Solion: Fis mlil his qaion b (whih w an do sin > o ansfom i ino h Cah- El qaion givn b w ( 6w ( 4 Thn b making h sbsiion (and sing qaion (7 on ag 88 of h,
Study of Tyre Damping Ratio and In-Plane Time Domain Simulation with Modal Parameter Tyre Model (MPTM)
Sudy o Ty Damping aio and In-Plan Tim Domain Simulaion wih Modal Paam Ty Modl (MPTM D. Jin Shang, D. Baojang Li, and Po. Dihua Guan Sa Ky Laboaoy o Auomoiv Say and Engy, Tsinghua Univsiy, Bijing, China
Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is
39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h
Partial Fraction Expansion
Paial Facion Expanion Whn ying o find h inv Laplac anfom o inv z anfom i i hlpfl o b abl o bak a complicad aio of wo polynomial ino fom ha a on h Laplac Tanfom o z anfom abl. W will illa h ing Laplac anfom.
1 Lecture: pp
EE334 - Wavs and Phasos Lcu: pp -35 - -6 This cous aks vyhing ha you hav bn augh in physics, mah and cicuis and uss i. Easy, only nd o know 4 quaions: 4 wks on fou quaions D ρ Gauss's Law B No Monopols
On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument
Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
EXERCISE - 01 CHECK YOUR GRASP
DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc
Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule
Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -
Elementary Differential Equations and Boundary Value Problems
Elmnar Diffrnial Equaions and Boundar Valu Problms Boc. & DiPrima 9 h Ediion Chapr : Firs Ordr Diffrnial Equaions 00600 คณ ตศาสตร ว ศวกรรม สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา /55 ผศ.ดร.อร ญญา ผศ.ดร.สมศ
Investment. Net Present Value. Stream of payments A 0, A 1, Consol: same payment forever Common interest rate r
Bfo going o Euo on buin, a man dov hi Roll-Royc o a downown NY Ciy bank and wn in o ak fo an immdia loan of $5,. Th loan offic, akn aback, qud collaal. "Wll, hn, h a h ky o my Roll-Royc", h man aid. Th
Lecture 2: Current in RC circuit D.K.Pandey
Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging
Lecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey
cur : Growh and dcay of currn in circui Growh of currn in Circui us considr an inducor of slf inducanc is conncd o a DC sourc of.m.f. E hrough a rsisr of rsisanc and a ky K in sris. Whn h ky K is swichd
Double Slits in Space and Time
Doubl Slis in Sac an Tim Gorg Jons As has bn ror rcnly in h mia, a am l by Grhar Paulus has monsra an inrsing chniqu for ionizing argon aoms by using ulra-shor lasr ulss. Each lasr uls is ffcivly on an
Lecture-V Stochastic Processes and the Basic Term-Structure Equation 1 Stochastic Processes Any variable whose value changes over time in an uncertain
Lecue-V Sochasic Pocesses and he Basic Tem-Sucue Equaion 1 Sochasic Pocesses Any vaiable whose value changes ove ime in an unceain way is called a Sochasic Pocess. Sochasic Pocesses can be classied as
GUIDE FOR SUPERVISORS 1. This event runs most efficiently with two to four extra volunteers to help proctor students and grade the student
GUIDE FOR SUPERVISORS 1. This vn uns mos fficinly wih wo o fou xa voluns o hlp poco sudns and gad h sudn scoshs. 2. EVENT PARAMETERS: Th vn supviso will povid scoshs. You will nd o bing a im, pns and pncils
Instructors Solution for Assignment 3 Chapter 3: Time Domain Analysis of LTIC Systems
Inrucor Soluion for Aignmn Chapr : Tim Domain Anali of LTIC Sm Problm i a 8 x x wih x u,, an Zro-inpu rpon of h m: Th characriic quaion of h LTIC m i i 8, which ha roo a ± j Th zro-inpu rpon i givn b zi
3.4 Repeated Roots; Reduction of Order
3.4 Rpd Roos; Rducion of Ordr Rcll our nd ordr linr homognous ODE b c 0 whr, b nd c r consns. Assuming n xponnil soluion lds o chrcrisic quion: r r br c 0 Qudric formul or fcoring ilds wo soluions, r &
4. AC Circuit Analysis
4. A icui Analysis J B A Signals sofquncy Quaniis Sinusoidal quaniy A " # a() A cos (# + " ) ampliud : maximal valu of a() and is a al posiiv numb; adian [/s]: al posiiv numb; phas []: fquncy al numb;
Copyright 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Chapr Rviw 0 6. ( a a ln a. This will qual a if an onl if ln a, or a. + k an (ln + c. Thrfor, a an valu of, whr h wo curvs inrsc, h wo angn lins will b prpnicular. 6. (a Sinc h lin passs hrough h origin
An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT
[Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI
UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o
Midterm exam 2, April 7, 2009 (solutions)
Univrsiy of Pnnsylvania Dparmn of Mahmaics Mah 26 Honors Calculus II Spring Smsr 29 Prof Grassi, TA Ashr Aul Midrm xam 2, April 7, 29 (soluions) 1 Wri a basis for h spac of pairs (u, v) of smooh funcions
Review Lecture 5. The source-free R-C/R-L circuit Step response of an RC/RL circuit. The time constant = RC The final capacitor voltage v( )
Rviw Lcur 5 Firs-ordr circui Th sourc-fr R-C/R-L circui Sp rspons of an RC/RL circui v( ) v( ) [ v( 0) v( )] 0 Th i consan = RC Th final capacior volag v() Th iniial capacior volag v( 0 ) Volag/currn-division
CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano
Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER14 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th
CSE 245: Computer Aided Circuit Simulation and Verification
CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy
REPETITION before the exam PART 2, Transform Methods. Laplace transforms: τ dτ. L1. Derive the formulas : L2. Find the Laplace transform F(s) if.
Tranform Mhod and Calculu of Svral Variabl H7, p Lcurr: Armin Halilovic KTH, Campu Haning E-mail: armin@dkh, wwwdkh/armin REPETITION bfor h am PART, Tranform Mhod Laplac ranform: L Driv h formula : a L[
Fig. 1S. The antenna construction: (a) main geometrical parameters, (b) the wire support pillar and (c) the console link between wire and coaxial
a b c Fig. S. The anenna consucion: (a) ain geoeical paaees, (b) he wie suppo pilla and (c) he console link beween wie and coaial pobe. Fig. S. The anenna coss-secion in he y-z plane. Accoding o [], he
H is equal to the surface current J S
Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion
P a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
Adrian Sfarti University of California, 387 Soda Hall, UC Berkeley, California, USA
Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Rliisi Dnis n lonis in Unifol l n in Unifol Roin s-th Gnl ssions fo h loni 4-Vo Ponil in Sfi Unisi of Clifoni 387 So Hll UC Bkl Clifoni US s@ll.n
On the Speed of Heat Wave. Mihály Makai
On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.
3: Theory of Pressure Gradient Microphones
On h Tho of h Scond-Od Soundfild Micohon Phili Coll : Tho of Pu Gadin Micohon In an iooic mdium uch a ai, h ound u a a oin du o h oagaion of a ound wav i indndn of h dicion in which h wav avl hough ha
Charging of capacitor through inductor and resistor
cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.
A Simple Method for Determining the Manoeuvring Indices K and T from Zigzag Trial Data
Rind 8-- Wbsi: wwwshimoionsnl Ro 67, Jun 97, Dlf Univsiy of chnoloy, Shi Hydomchnics Lbooy, Mklw, 68 CD Dlf, h Nhlnds A Siml Mhod fo Dminin h Mnouvin Indics K nd fom Ziz il D JMJ Jouné Dlf Univsiy of chnoloy
S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]
![S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]](/thumbs/92/108666103.jpg "S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]")
S.Y. B.Sc. (IT) : Sm. III Applid Mahmaics Tim : ½ Hrs.] Prlim Qusion Papr Soluion [Marks : 75 Q. Amp h following (an THREE) 3 6 Q.(a) Rduc h mari o normal form and find is rank whr A 3 3 5 3 3 3 6 Ans.:
Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.
Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.
AQUIFER DRAWDOWN AND VARIABLE-STAGE STREAM DEPLETION INDUCED BY A NEARBY PUMPING WELL
Pocing of h 1 h Innaional Confnc on Enionmnal cinc an chnolog Rho Gc 3-5 pmb 15 AUIFER DRAWDOWN AND VARIABE-AGE REAM DEPEION INDUCED BY A NEARBY PUMPING WE BAAOUHA H.M. aa Enionmn & Eng Rach Iniu EERI
ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
General Non-Arbitrage Model. I. Partial Differential Equation for Pricing A. Traded Underlying Security
1 Geneal Non-Abiage Model I. Paial Diffeenial Equaion fo Picing A. aded Undelying Secuiy 1. Dynamics of he Asse Given by: a. ds = µ (S, )d + σ (S, )dz b. he asse can be eihe a sock, o a cuency, an index,
Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016
Applid Saisics and robabiliy for Enginrs, 6 h diion Ocobr 7, 6 CHATER Scion - -. a d. 679.. b. d. 88 c d d d. 987 d. 98 f d.. Thn, = ln. =. g d.. Thn, = ln.9 =.. -7. a., by symmry. b.. d...6. 7.. c...
Control System Engineering (EE301T) Assignment: 2
Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also
ADDITIVE INTEGRAL FUNCTIONS IN VALUED FIELDS. Ghiocel Groza*, S. M. Ali Khan** 1. Introduction
ADDITIVE INTEGRAL FUNCTIONS IN VALUED FIELDS Ghiocl Goza*, S. M. Ali Khan** Abstact Th additiv intgal functions with th cofficints in a comlt non-achimdan algbaically closd fild of chaactistic 0 a studid.
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
Derivation of the differential equation of motion
Divion of h iffnil quion of oion Fis h noions fin h will us fo h ivion of h iffnil quion of oion. Rollo is hough o -insionl isk. xnl ius of h ll isnc cn of ll (O) - IDU s cn of gviy (M) θ ngl of inclinion
OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
The Black-Scholes Formula
lack & chols h lack-chols Fomula D. Guillmo Lópz Dumauf dumauf@fibl.com.a Copyigh 6 by D. Guillmo Lópz Dumauf. No pa of his publicaion may b poducd, sod in a ival sysm, o ansmid in any fom o by any mans
Equation For non-self Energizing Gasket
Jun 0 0:05: - ASMEScDiv_WNFlangDsign.sm Dsign of Wld Nck Flang as pr ASME Scion Division ar.6 Dsign ol oads STE : Dsign ondiion Dsign rssur 0. Ma Dsign Tmpraur T 80 d STE : ask Facors 'm' and Minimum Dsign
Math 3301 Homework Set 6 Solutions 10 Points. = +. The guess for the particular P ( ) ( ) ( ) ( ) ( ) ( ) ( ) cos 2 t : 4D= 2
Mah 0 Homwork S 6 Soluions 0 oins. ( ps) I ll lav i o you o vrify ha y os sin = +. Th guss for h pariular soluion and is drivaivs is blow. Noi ha w ndd o add s ono h las wo rms sin hos ar xaly h omplimnary
X-CAPM: An Extrapolative Capital Asset Pricing Model
X-CAPM: An Exapolaiv Capial Ass Picing Modl Nicholas Babis*, Robin Gnwood**, Lawnc Jin*, and Andi Shlif** *Yal Univsiy and **Havad Univsiy Absac Suvy vidnc suggss ha many invsos fom blifs abou fuu sock
CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A. Ήχος Πα. to os se e e na aș te e e slă ă ă vi i i i i
CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A Ήχος α H ris to os s n ș t slă ă ă vi i i i i ți'l Hris to o os di in c ru u uri, în tâm pi i n ți i'l Hris
Homework 2 Solutions
Mah 308 Differenial Equaions Fall 2002 & 2. See he las page. Hoework 2 Soluions 3a). Newon s secon law of oion says ha a = F, an we know a =, so we have = F. One par of he force is graviy, g. However,
The Exile Began. Family Journal Page. God Called Jeremiah Jeremiah 1. Preschool. below. Tell. them too. Kids. Ke Passage: Ezekiel 37:27
Faily Jo Pag Th Exil Bg io hy u c prof b jo ou Shar ab ou job ab ar h o ay u Yo ra u ar u r a i A h ) ar par ( grp hav h y y b jo i crib blo Tll ri ir r a r gro up Allo big u r a i Rvi h b of ha u ha a
Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison
Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd
A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER
A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:
Time-Space Model of Business Fluctuations
Time-Sace Moel of Business Flucuaions Aleei Kouglov*, Mahemaical Cene 9 Cown Hill Place, Suie 3, Eobicoke, Onaio M8Y 4C5, Canaa Email: Aleei.Kouglov@SiconVieo.com * This aicle eesens he esonal view of
Shor s Algorithm. Motivation. Why build a classical computer? Why build a quantum computer? Quantum Algorithms. Overview. Shor s factoring algorithm
Motivation Sho s Algoith It appas that th univs in which w liv is govnd by quantu chanics Quantu infoation thoy givs us a nw avnu to study & tst quantu chanics Why do w want to build a quantu coput? Pt
MA 214 Calculus IV (Spring 2016) Section 2. Homework Assignment 1 Solutions
MA 14 Calculus IV (Spring 016) Secion Homework Assignmen 1 Soluions 1 Boyce and DiPrima, p 40, Problem 10 (c) Soluion: In sandard form he given firs-order linear ODE is: An inegraing facor is given by
X-CAPM: An Extrapolative Capital Asset Pricing Model
X-CAPM: An Exapolaiv Capial Ass Picing Modl Nicholas Babis*, Robin Gnwood**, Lawnc Jin*, and Andi Shlif** *Yal Univsiy and **Havad Univsiy Mach 6, 4 Absac Suvy vidnc suggss ha many invsos fom blifs abou
FOR MORE PAPERS LOGON TO
IT430 - E-Commerce Quesion No: 1 ( Marks: 1 )- Please choose one MAC sand for M d a A ss Conro a M d a A ss Consor M r of As an Co n on of s Quesion No: 2 ( Marks: 1 )- Please choose one C oos orr HTML
( ) ( ) + = ( ) + ( )
Mah 0 Homwork S 6 Soluions 0 oins. ( ps I ll lav i o you vrify ha h omplimnary soluion is : y ( os( sin ( Th guss for h pariular soluion and is drivaivs ar, +. ( os( sin ( ( os( ( sin ( Y ( D 6B os( +
Final Exam. Thursday, December hours, 30 minutes
San Faniso Sa Univsi Mihal Ba ECON 30 Fall 0 Final Exam husda, Dmb 5 hous, 30 minus Nam: Insuions. his is losd book, losd nos xam.. No alulaos of an kind a allowd. 3. Show all h alulaions. 4. If ou nd
An Asymptotic Expansion for the Non-Central Chi-square Distribution. By Jinan Hamzah Farhood Department of Mathematics College of Education
A Asypoic Expasio fo h o-cal Chi-squa Disibuio By Jia Hazah ahood Dpa of Mahaics Collg of Educaio 6 Absac W div a asypoic xpasio fo h o-cal chi-squa disibuio as wh X i is h o-cal chi-squa vaiabl wih dg
UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.
UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM Solution (TEST SERIES ST PAPER) Dat: No 5. Lt a b th adius of cicl, dscibd by th aticl P in fig. if, a th ola coodinats of P, thn acos Diffntial
Homework 10 (Stats 620, Winter 2017) Due Tuesday April 18, in class Questions are derived from problems in Stochastic Processes by S. Ross.
Homework (Sas 6, Winer 7 Due Tuesday April 8, in class Quesions are derived from problems in Sochasic Processes by S. Ross.. A sochasic process {X(, } is said o be saionary if X(,..., X( n has he same
Combinatorial Approach to M/M/1 Queues. Using Hypergeometric Functions
Inenaional Mahemaical Foum, Vol 8, 03, no 0, 463-47 HIKARI Ld, wwwm-hikaicom Combinaoial Appoach o M/M/ Queues Using Hypegeomeic Funcions Jagdish Saan and Kamal Nain Depamen of Saisics, Univesiy of Delhi,
Fundamental Vehicle Loads & Their Estimation
Fundaenal Vehicle Loads & Thei Esiaion The silified loads can only be alied in he eliinay design sage when he absence of es o siulaion daa They should always be qualified and udaed as oe infoaion becoes
Einstein s Field Equations in Cosmology Using Harrison s Formula
Ein s ild Equaions in Cosmoloy U Haison s omula Ioannis Ialis Haanas, Dpamn of Physis and sonomy Yo Univsiy, Tno, Onaio, Canada E-mail: ioannis@you.a bsa Th mos impoan l fo h sudy of h aviaional fild in
a dt a dt a dt dt If 1, then the poles in the transfer function are complex conjugates. Let s look at f t H t f s / s. So, for a 2 nd order system:
Undrdamd Sysms Undrdamd Sysms nd Ordr Sysms Ouu modld wih a nd ordr ODE: d y dy a a1 a0 y b f If a 0 0, hn: whr: a d y a1 dy b d y dy y f y f a a a 0 0 0 is h naural riod of oscillaion. is h daming facor.
2. The Laplace Transform
Th aac Tranorm Inroucion Th aac ranorm i a unamna an vry uu oo or uying many nginring robm To in h aac ranorm w conir a comx variab σ, whr σ i h ra ar an i h imaginary ar or ix vau o σ an w viw a a oin
y = (y 1)*(y 3) t
MATH 66 SPR REVIEW DEFINITION OF SOLUTION A funcion = () is a soluion of he differenial equaion d=d = f(; ) on he inerval ff < < fi if (d=d)() =f(; ()) for each so ha ff
Midterm Examination (100 pts)
Econ 509 Spring 2012 S.L. Parn Midrm Examinaion (100 ps) Par I. 30 poins 1. Dfin h Law of Diminishing Rurns (5 ps.) Incrasing on inpu, call i inpu x, holding all ohr inpus fixd, on vnuall runs ino h siuaion
4.5 Constant Acceleration
4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),
x y θ = 31.8 = 48.0 N. a 3.00 m/s
4.5.IDENTIY: Vecor addiion. SET UP: Use a coordinae sse where he dog A. The forces are skeched in igure 4.5. EXECUTE: + -ais is in he direcion of, A he force applied b =+ 70 N, = 0 A B B A = cos60.0 =
On the Integro-Differential Equation with a Bulge Function by Using Laplace Transform
Applied Mahemaical Sciences, Vol. 9, 15, no. 5, 9-34 HIKARI Ld, www.m-hikari.com hp://dx.doi.org/1.1988/ams.15.411931 On he Inegro-Differenial Equaion wih a Bulge Funcion by Using Laplace Transform P.
The airship maintenance with its renovation and the risk of its loss
Commns on h impovmn of h miliay aicaf opaion by iing... 9 RELIABILITY SCIENTIFIC ROBLEMS OF MACHINES OERATION AND MAINTENANCE 4 (56) 008 HENRYK TOMASZEK * JÓZEF ŻUREK * SŁAWOMIR STĘIEŃ ** Th aiship mainnanc
Wave Equation (2 Week)
Rfrnc Wav quaion ( Wk 6.5 Tim-armonic filds 7. Ovrviw 7. Plan Wavs in Losslss Mdia 7.3 Plan Wavs in Loss Mdia 7.5 Flow of lcromagnic Powr and h Poning Vcor 7.6 Normal Incidnc of Plan Wavs a Plan Boundaris
Institute of Actuaries of India
Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6
ENV 6015 Solution to Mixing Problem Set
EN 65 Soluion o ixing Problem Se. A slug of dye ( ) is injeced ino a single ank wih coninuous mixing. The flow in and ou of he ank is.5 gpm. The ank volume is 5 gallons. When will he dye concenraion equal
Executive Committee and Officers ( )
Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r
Lecture 20. Transmission Lines: The Basics
Lcu 0 Tansmissin Lins: Th Basics n his lcu u will lan: Tansmissin lins Diffn ps f ansmissin lin sucus Tansmissin lin quains Pw flw in ansmissin lins Appndi C 303 Fall 006 Fahan Rana Cnll Univsi Guidd Wavs
X-CAPM: An Extrapolative Capital Asset Pricing Model
X-CAPM: An Exapolaiv Capial Ass Picing Modl Th Havad communiy has mad his aicl opnly availabl. Plas sha how his accss bnfis you. You soy mas. Ciaion Publishd Vsion Accssd Ciabl Link Tms of Us Babis, Nicholas,
Chapter 1 Basic Concepts
Ch Bsc Cocs oduco od: X X ε ε ε ε ε O h h foog ssuos o css ε ε ε ε ε N Co No h X Chcscs of od: cos c ddc (ucod) d s of h soss dd of h ssocd c S qusos sd: Wh f h cs of h soss o cos d dd o h ssocd s? Wh
4. AC Circuit Analysis
4. A icui Analysis J B Dpamn of Elcical, Elconic, and nfomaion Engining (DE) - Univsiy of Bologna A Signals sofquncy Quaniis Sinusoidal quaniy A q w a() A cos ( w + q ) ampliud : maximal valu of a() and
Chapter 4 Longitudinal static stability and control Effect of acceleration (Lecture 15)
Chapr 4 Longiudinal saic sabiliy and conrol Effc of acclraion (Lcur 15) Kywords : Elvaor rquird in pull-up; sick-fixd manuvr poin; sick forc gradin in pull-up; manuvr poin sick-fr; ovrall limis on c.g.
University of Toledo REU Program Summer 2002
Univiy of Toldo REU Pogam Summ 2002 Th Effc of Shadowing in 2-D Polycyallin Gowh Jff Du Advio: D. Jacqu Ama Dpamn of Phyic, Univiy of Toldo, Toldo, Ohio Abac Th ffc of hadowing in 2-D hin film gowh w udid
Stochastic Modelling in Finance - Solutions to sheet 8
Sochasic Modelling in Finance - Soluions o shee 8 8.1 The price of a defaulable asse can be modeled as ds S = µ d + σ dw dn where µ, σ are consans, (W ) is a sandard Brownian moion and (N ) is a one jump
Chapter 2. First Order Scalar Equations
Chaper. Firs Order Scalar Equaions We sar our sudy of differenial equaions in he same way he pioneers in his field did. We show paricular echniques o solve paricular ypes of firs order differenial equaions.
Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri-
sh Wdsdy 7 gn mult- tú- st Frst Intrt thng X-áud m. ns ní- m-sr-cór- Ps. -qu Ptr - m- Sál- vum m * usqu 1 d fc á-rum sp- m-sr-t- ó- num Gló- r- Fí- l- Sp-rí- : quó-n- m ntr-vé-runt á- n-mm c * m- quó-n-
Results as of 30 September 2018
rt Results as of 30 September 2018 F r e e t r a n s l a t ion f r o m t h e o r ig ina l in S p a n is h. I n t h e e v e n t o f d i s c r e p a n c y, t h e Sp a n i s h - la n g u a g e v e r s ion
ME 391 Mechanical Engineering Analysis
Fall 04 ME 39 Mechanical Engineering Analsis Eam # Soluions Direcions: Open noes (including course web posings). No books, compuers, or phones. An calculaor is fair game. Problem Deermine he posiion of
WH2. Queensville West PS to WH2 WH2. Queensville West Pumping Station. Queensville Sid. Concession Road 2. Figure B.13
Quvill Si Quvill W S a Quvill W upi Sai xc_x25_1_fcai_pfil p u Quvil W upi Sai Map L ' ci a 2 Fiu B.13 a Suiabl f Wa Rclaai 12 buff f Gbl Naual Hia S Quvill W upi Sai 12 buff f Siifica W a UYSS Svic a
H STO RY OF TH E SA NT
O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922
CHAPTER 9 Compressible Flow
CHPTER 9 Comrssibl Flow Char 9 / Comrssibl Flow Inroducion 9. c c cv + R. c kcv. c + R or c R k k Rk c k Sd of Sound 9.4 Subsiu Eq. 4.5.8 ino Eq. 4.5.7 and nglc onial nrgy chang: Q WS + + u~ u~. m ρ ρ
Challenge Problems. DIS 203 and 210. March 6, (e 2) k. k(k + 2). k=1. f(x) = k(k + 2) = 1 x k
Challenge Problems DIS 03 and 0 March 6, 05 Choose one of he following problems, and work on i in your group. Your goal is o convince me ha your answer is correc. Even if your answer isn compleely correc,