Keldysh Formalism: Nonequilibrium Green s Function


 Iris Barber
 3 years ago
 Views:
Transcription
1 Keldysh Formalism: Nonequilibrium Green s Funcion Jinshan Wu Deparmen of Physics & Asronomy, Universiy of Briish Columbia, Vancouver, B.C. Canada, V6T 1Z1 (Daed: November 28, 2005) A review of Nonequilibrium Green s Funcion (NEGF), also named as Keldysh Formalism, is presened here. Perurbaion heory is also builded up sep by sep on he basis of nonineracing NEGF, and hen leads o he Dyson s Equaion. Finally, applicaion of NEGF on ighbinding model wih random impuriy is explicily calculaed as an example. I. DEFINITION, FREE FIELD AND PERTURBATION When only he properies of ground sae is concerned, Zeroemperaure (single and manyparicle) Green s funcion ogeher wih is perurbaion heory principally gives all he informaion. Also if he equilibrium hermal disribuion is concerned, we can urn o Masubara Green s funcion and is perurbaion heory[2]. However, we may need o consider some more general saes, such as a saionary nonequilibrium sae for example a sae wih nonzero curren, or even an arbirary sae ρ, how o ge correlaion funcion for such sysem and hen how o do he corresponding perurbaion expansion? In experimens of conduciviy, here are such nonequilibrium sysem, which has nonzero curren and includes ineracion beween paricles. So in his noe I will shorly review he idea and echnics of Nonequilibrium Green s funcion, also known as Keldysh Formalism. All he formulas defined in his noe is only for fermions, alhough i is no hard o make hem o also cover bosons. Generally we need o calculae he Green s funcion G (x, ; x, ) = i } ) (T T r ψ H (x, ) ψ H (x, ) ρ H, (1) where ψ H (x, ) is he annihilaion operaor in Heisenberg picure, and ρ is he densiy marix also in Heisenberg picure. We will se = 1 for a while. We also assume ρ is diagonal under paricle number basis, [N, ρ] = 0. More general densiy marix could be possible, bu no used anywhere ye. For free field, his can be calculaed quie srai forward, ha ψh (x, ) = k e iω(k)+ikx c k ψ H (x, ) = k eiω(k) ikx c, (2) k hen G 0 (x, ; x, ) = iθ ( ) k 1 n k e iω(k)( )+ik(x x ) iθ ( ) k n k e iω(k)( )+ik(x x ) (3) Following he roadmap of zeroemperaure Green s funcion, nex sep would be o urn ψ H (x, ) ino ineracion picure ψ I (x, ) and o somehow replace he real sae ρ H wih sae of nonineracing sysem ρ 0 H. Le s firs organize he above mapping for zeroemperaure Green s funcion and hen see if he same procedure can be applied ono NEGF. Zeroemperaure Green s funcion is defined as a special case of eq(1), ρ H = Ω Ω, } G (x, ; x, ) = i Ω T ψ H (x, ) ψ H (x, ) Ω, (4) Firs, express T A H ( 1 ) B H ( 2 )} in ineracion picure. and H = H 0 + e ɛ 0 H 1, (5) A H () = e ih( 0) e ih0( 0) A I () e ih0( 0) e ih( 0). (6)
2 2 FIG. 1: The imeloop inegraion pah. Define uniary operaor U (, ) = e ih0( 0) e ih( 0) e ih0( 0), (7) which is he formal soluion of where H I () = e ih0( 0) H 1 e ih0( 0). Or he explici form is Then for 1 > 2 he imeordered operaors, i U (, ) = H I () U (, ), (8) U (, ) = T exp i dh I (). (9) T A H ( 1 ) B H ( 2 )} = A H ( 1 ) B H ( 2 ) = U ( 1, 0 ) A I ( 1 ) U ( 1, 0 ) U ( 2, 0 ) B I ( 2 ) U ( 2, 0 ) = U ( 0, 1 ) A I ( 1 ) U ( 1, 2 ) B I ( 2 ) U ( 2, 0 ). (10) = U ( 0, ) U (, 1 ) A I ( 1 ) U ( 1, 2 ) B I ( 2 ) U ( 2, ) U (, 0 ) Nex for rue ground sae Ω, we can relae i wih 0, he ground sae of nonineracing field, U ( 0, ) 0 = lim T eih( T 0) e ih0( T 0) 0 = lim T e ih(t +0) 0. (11) According o GellMann and Low Theorem, for adiabaic coupling, back in Schrödinger picure, ground sae is sable, φ 0 ( f ) U ( f, i ) φ 0 ( i ). In our case, Ω ( 0 ) U ( 0, T ) 0 ( T ), so up o some consan, U ( 0, ) 0 Ω U (, 0 ) Ω 0, (12) and similarly, U (, 0 ) Ω 0. Therefore, when 1 > 2 } Ω T ψ H (x, ) ψ H (x, ) Ω 0 U (, 1 ) A I () U ( 1, 2 ) B I () U ( 2, ) 0. (13) Finally, he consan can be eliminaed as 0 T G (x, ; x, ) = i } ψ I (x, ) ψ I (x, ) U (, ) 0 U (, ) 0 0, (14) where now all he quaniies are from free field, and herefore can be calculaed order by order by perurbaion. However, when we apply he same procedure o general ρ H, we require he GellMann and Low heorem holds for excied saes for boh = ±. This condiion is oo srong. The idea o solve above problem is o remove some special poins from he hree special poins = (, 0, ), for example by seing 0. In his way we require ha only φ 0 () = 0 insead of boh φ 0 (± ) = 0. The pah is o sar along = o = 0 and hen come back along = 0 o =. And finally le 0, a picured in fig(1). As inhe case of usual Green s funcion, le firsly reorganize T A ( 1 ) B ( 2 )}, and hen he relaion beween ρ H and ρ 0 H. For 1 > 2, inser U (, ) ino eq(10), T A H ( 1 ) B H ( 2 )} = U ( 0, ) U (, ) U (, 1 ) A I ( 1 ) U ( 1, 2 ) B I ( 2 ) U ( 2, )} U (, 0 ). (15) Then boh sides relaes only wih U (, 0 ), which sill link he rue eigensaes n wih freefield eigensaes n 0, ha U (, 0 ) n n 0. (16)
3 3 (a) G + (, ) and G (, ) (b)g c (, ) (c) G c (, ) s (d) Impuriy Scaering FIG. 2: One possible Feynman rules for NEGF. Therefore, we arrive G (x, ; x, ) = i T r(u(, )Tψ I (x,)ψ I(x, )U(,)}ρ 0 H) T r(u(,)ρ 0 H) = i T r(tcψ I (x,)ψ I(x, )U(,)}ρ 0 H) T r(u(,)ρ 0 H), (17) where T c is he loop order as shown in fig(1) o order he ime along he loop from o. For example, a he above branch i s he same wih ime order T c = T, while a he lower branch i s aniime order T c = T. And U (, ) = T c exp i dhi (). (18) One hing need o be noiced ha in he final expression of Green s funcion, all he ime spos should be reaed as poins a above branch (also call posiive branch). However, laer on, we will see ha when we ry o calculae such Green s funcion, we will need o do inegral also over he lower branch (also call negaive branch). This means generally no all he ime spos are a he posiive branch, and he second line of eq(17) could no be separaed as U (, ) and U (, ) ouside and inside usual ime order T. Therefore, generally we need o define Green s funcion according o he branches of and. There are four differen configuraions of hem, as picured in fig(2). They are less and greaer Green s funcion[1], G + (x, ; x, ) = it r (ρ H T c ψ H (x, + ) ψ ( ) ( ) H x, = it r ρ H ψ H (x, ) ψ H (x, ) G (x, ; x, ) = it r (ρ H T c ψ H (x, ) ψ ( ) ( ), (19) H x, + = it r ρ H ψ H (x, ) ψ H (x, ) where ± means he ime is on posiive/negaive branch; ime ordered and aniime ordered Green s funcion, G c (x, ; x, ) = it r (ρ H T c ψ H (x, + ) ψ ( ) ( H x, + = it r ρ H T ψ H (x, ) ψ H (x, ) G c (x, ; x, ) = it r (ρ H T c ψ H (x, ) ψ ( ) ( ; (20) H x, = it r ρ H T ψ H (x, ) ψ H (x, )
4 and rearded and advanced Green s funcion, G r (x, ; x, ) = iθ ( ) T r (ρ H ψ H (x, ), ψ H (x, ). (21) G a (x, ; x, ) = iθ ( ) T r (ρ H ψ H (x, ), ψ H (x, ) Only hree of hem are independen, G r = G c G + = G G c, G a = G c G = G + G c. (22) This can be seen easily by separaing G ± as four pars, θ ( ) G ± and θ ( + ) G ±. Then G c = θ ( + ) G + + θ ( ) G G c = θ ( ) G + + θ ( + ) G (23) So G c + G c = G + + G. Noice for greaer/less Green s funcion, differen definiions and noaions are used in lieraure, for example, G > G and G < G + in [2]. Before we go furher o perurbaion calculaion of ineracing field, le s firs lis all he freefield Nonequilibrium Green s funcions. 4 G 0,+ (x, ; x, ) = i k n k e iω(k)( )+ik(x x ) G 0, (x, ; x, ) = i k 1 n k e iω(k)( )+ik(x x ) G 0,c (x, ; x, ) = i k θ ( ) n k e iω(k)( )+ik(x x ) G 0, c (x, ; x, ) = i k θ ( ) n k e iω(k)( )+ik(x x ) G 0,r (x, ; x, ) = iθ ( ) k e iω(k)( )+ik(x x ) G 0,a (x, ; x, ) = iθ ( ) k e iω(k)( )+ik(x x ) (24) Abou Eq(16), he expression similar wih of GellMann and Low Theorem, i should be undersood in a kind inverse logic order. For an ineracing field H = H 0 + H 1, he nonequilibrium densiy marix ρ H is no clearly defined, while ρ 0 H of he corresponding free filed H 0 could be well defined. Then he meaning of eq(16) is ha we sar from ρ 0 H a = and arrive a sae a = 0, and hen jus use his new sae as ρ H. I s no guaraneed ha his reamen will correspond o he rue nonequilibrium disribuion ρ H. So for NEGF, even concepually insead of saring from he rue ρ H, we build up he heory from ρ 0 H. This could be a disadvanage of NEGF. Also several advanages need o be noiced. Firs, his NEGF can be used for sysem a hermal equilibrium sae, which is usually he subjec of Masubara Green s funcion. We will use as an example in III. Second, even H 1 explicily depends on, his NEFG is sill applicable, because we only se one end as H 1 () = 0, H 1 ( ) could be arbirary. A las, for nonequilibrium sysem as long as a unambiguous freefield corresponding nonequilibrium sae could be defined, we could always do he perurbaion calculaion order by order. II. SELFENERGY AND DYSON S EQUATION In order o arrive a he Dyson s equaion, we would firsly go o a lile pracice of firs and second order calculaion. Consider an example wih V = αβ M αβc αc β [2]. Then he firs order perurbaion gives, G + (µ, ; ν, ) = G 0,+ (µ, ; ν, ) dsm αβ T r ( T c Cµ () C ν ( ) C α (s) C β (s). (25) αβ The second erm has one disconneced erm and one nonzero conneced erm, which includes αβ dsmαβ Tc Cµ () C α (s) } T c C ν ( ) C β (s) } = [ αβ dsg0,c (µ, ; α, s) M αβ G 0,+ (β, s; ν, ) + ] dsg0,+ (µ, ; α, s) M αβ G 0, c (β, s; ν, ) (26) A he nex order, more erms will be coupled ino his expansion series. Similarly G also couples wih all oher Gs. We will work ou explicily a special case of his ineracion in he nex secion III. Skipping some deailed calculaion here, overall hese expansion series could be represened by a marix equaion, in he form of ( ) Ĝ = Ĝ0ΣĜ0 + Ĝ0ΣĜ0ΣĜ0 + = Ĝ0 1 + ΣĜ (27)
5 5 Like he example abou disordered sysem in lecure noes[3], concep of selfenergy Σ can be inroduced. Then he Dyson s equaion of NEGF could be organized as Ĝ (, ) = Ĝ0 (, ) + d 1 d 2 Ĝ 0 (, 1 ) ˆΣ ( 1, 2 ) Ĝ ( 2, ), (28) where ( Ĝc Ĝ Ĝ = Ĝ + Ĝ c ), (29) and Ĝ (, ) is he operaor form of G (x, ; x, ) = x Ĝ (, ) x ; Ĝ 0 = ˆD is he freefield NEGF; and ˆΣ is he selfenergy erm coming from ineracion, ( ) ˆΣc ˆΣ ˆΣ = ˆΣ +. (30) ˆΣ c We will explain boh heoreically and by examples how o ge he selfenergy erm from ineracion laer. Le s emporally suppose hey are known. Because only hree are independen of hese six NEGFs, he above formula can be simplified furher by choosing he righ hree independen ones. Le s use Ĝa, Ĝr and From eq(22) i is easy o see ha his ransformaion is uniary, ( Ĝc Ĝ U Ĝ + Ĝ c ˆF = Ĝc + Ĝ c. (31) ) ( ) U 0 Ĝ = a Ĝ r Ǧ, (32) ˆF where U = 1 ( ) 1 1. (33) Induced by his ransformaion, he selfenergy erm will ransform as ( ) ˆΣc ˆΣ ˇΣ U ˆΣ + U, (34) ˆΣ c And finally, as we will see from he example in secion III, because generally Σ c + Σ c = (Σ + + Σ ), ( ) Ω Σ r ˇΣ Σ a, (35) 0 Therefore, eq(28) sill holds, bu in a new form, or simply denoed as, Ǧ = Ǧ0 + Ǧ0 ˇΣǦ. (36) Then he calculaion of Green s funcion becomes calculaion of selfenergy, where differen approximaions, such as Born or SelfConsisen Born approximaion, could be used. III. EXAMPLE Le s apply he general procedure above ono he following problem, he random impuriy, a special case of he example in secion II, H = k ɛ (k) C k C k + k,q,x M (q) e iq X C k+q V C k, (37)
6 6 s s FIG. 3: Firs order expansion on loop pah, LHS for s on posiive branch, RHS for s on negaive branch. Boh of hem are zero if M (0) = 0. s 1 s 2 s 1 s 2 FIG. 4: Second order expansion of G + on loop pah, for s 1, s 2 boh on posiive branch. wih M (0) = 0 means average effec of impuriy is zero. X is uniformly disribued so ha k is sill a good quanum number, so G 0 (k, ; k, ) = G 0 (k, ; k, ) δ (k k ) and G (k, ; k, ) = G (k, ; k, ) δ (k k ). Le s firs work in ime domain, laer on we will do he Fourier ransformaion o work in he frequency domain. Firs order expansion of G +, eq(26) for our special case will be X 1 V [ dsg 0,c (k, ; k, s) M (0) G 0,+ (k, s; k, ) + ] dsg 0,+ (k, ; k, s) M (0) G 0, c (k, s; k, ) = 0. (38) Or equivalenly by Feynman Diagram, as in fig(3). The second order expansion of G + is, i 2V 2 ds 1 ds 2 e iq1 X1 iq2 X2 M (q 1 ) M (q 2 ) C k 1,q 1,X 1 k 2,q 2,X 2 T r (T, (39) c C k () C k ( ) C k 1+q 1 (s 1 ) C k1 (s 1 ) C k 2+q 2 (s 2 ) C k2 (s 2 ) where by Wick s Theorem, = T r +T r C k () C k 2+q 2 (s 2 ) T r T r C k () C k 1+q 1 (s 1 ) T r C k () C k ( ) C k 1+q 1 (s 1 ) C k1 (s 1 ) C k 2+q 2 (s 2 ) C k2 (s 2 ) C k1 (s 1 ) C k ( ) T r T r C k2 (s 2 ) C k ( ) C k2 (s 2 ) C k 1+q 1 (s 1 ). (40) C k1 (s 1 ) C k 2+q 2 (s 2 ) This has o be calculaed for he four configuraions of s 1, s 2. For example, here le s work ou for case of boh s 1, s 2 on posiive branch. i 2V 2 ds 1 ds 2 M (q 1 ) 2 e iq1 X1+iq1 X2 G 0,c (k, ; k, s 2 ) G 0,+ (k, s 1 ; k, ) G 0,c (k + q 1, s 2 ; k + q 1, s 1 ) q 1,X 1,X 2 + i 2V 2 ds 1 ds 2 M (q 2 ) 2 e iq2 X1 iq2 X2 G 0,c (k, ; k, s 1 ) G 0,+ (k, s 2 ; k, ) G 0,c (k + q 2, s 1 ; k + q 2, s 2 ). (41) q 2,X 1,X 2 = i V 2 ds 1 ds 2 M (q) 2 e iq X1 iq X2 G 0,c (k, ; k, s 1 ) G 0,+ (k, s 2 ; k, ) G 0,c (k + q, s 1 ; k + q, s 2 ) q,x 1,X 2 Those wo erm give he same conribuion because of he inegraion and summaion over s 1, s 2, q 1,2. Excep ha here G + couples wih G 0,c and ec, his expression has exacly he same form wih he second order of he usual
7 7 G + G G c G c NonZero Impuriy Line = Σ 1,c Σ 1, Σ 1, Σ 1, c FIG. 5: Anoher se of Feynman rules for NEGF, second order expansion is shown as example o express in hese new rules. Furher perurbaion could be done in his diagram form. Green s funcion wih impuriy. Similarly, G + also coupled wih G 0,, G 0, c and obviously G 0,+ iself. So par of he firs order of selfenergy erm could be defined as Σ c (k; s 2, s 1 ) i 2V 2 M (q 1 ) 2 e iq1 X1+iq1 X2 G 0,c (k + q, s 2 ; k + q, s 1 ). (42) q 1,X 1,X 2 So we ge a erm of G + a he second order in he form of If we check he erm abou G + in eq(28), we will ge G 2,+ = G 0,+ Σ 1,c G 0,c +... (43) G 2,+ = G 0,+ Σ 1,c G 0,c + G 0, c Σ 1,+ G 0,c + G 0,+ Σ 1, G 0,+ + G 0, c Σ 1, c G 0,+, (44) which does include he above erm we already calculaed. The diagram expression of all hose four erms are shown in he follow fig(5). A deail calculaion include all he configuraion of s 1, s 2 will give us he lef hree erms. Similarly we can do he second order expansion of G,c c. Then he hird order expansion will give us more selfenergy erms. Finally, we can ge he Dyson s equaion, which afer Fourier ransformaion will lead us o frequency domain Dyson s equaion. In he Feynman diagrams in fig(2), where he ime loop is explicily down o be an indicaor of he ype of Green s funcion. Besides his, considering he characer of our specific case, M (0) = 0, we may jus use differen lines o represen differen Green s funcions, so ha he diagrams could be simpler, Here we skip he boring derivaion of eq(36), he marix form Dyson s equaion, hopefully his will no sop one undersanding he general picure of NEGF. IV. SUMMARY Keldysh NEGF Formula is a generalizaion of he usual zero and nonzero emperaure Green s funcion. I can be applied ono he usual equilibrium cases and nonequilibrium case. The way we derive such formula here is o consruc a loop from o and back o, and inroducing Green s funcions G (, ) corresponding o he differen configuraion of (, ) over branches. Formally he srucure of Green s funcion and heir Dyson s Equaion
8 looks equivalen wih he one for usual Green s Funcion. So all he perurbaion calculaion is quie sraighforward. However, in order o do he perurbaion, a welldefined nonineracing sae and Green s funcion is a necessary saring poin. Wheher such saring poin leads o he real nonequilibrium sae is quesionable, and relies on he comparison beween calculaion and experimens. There is anoher way o ge his formula in [4], where he auhors use conour pah over complex plan o replace above loop pah. The derivaion is more elegan in a sense, bu he problem of picking up he righ saring poin sill exiss, alhough he auhors claim heir reamen is exac more or less. 8 [1] C. Caroli and R. Combresco and P. Nozieres and D. SainJames, Direc calculaion of he unneling curren, J. Phys. C: Solid S. Phys, 4(1971), [2] G. D. Manhan, ManyParicle Physics(1990 New York), Plenum Press. [3] M. Berciu, Lecure noes for Phys503, 2005, hp:// berciu/. [4] H. Haug and A.P. Jauho, Quanum Kineics in Transpor and Opics of Semiconducors(1996 Berlin Heidelberg), Springer Verlag.
Random Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationSignal Processing and Linear Systems I
Sanford Universiy Summer 214215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 1415, Gibbons
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More information2.5 Life tables, force of mortality and standard life insurance products
Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n
More informationEmergence of FokkerPlanck Dynamics within a Closed Finite Spin System
Emergence of FokkerPlanck Dynamics wihin a Closed Finie Spin Sysem H. Niemeyer(*), D. Schmidke(*), J. Gemmer(*), K. Michielsen(**), H. de Raed(**) (*)Universiy of Osnabrück, (**) Supercompuing Cener Juelich
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationOptimal Investment and Consumption Decision of Family with Life Insurance
Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker
More informationMaking Use of Gate Charge Information in MOSFET and IGBT Data Sheets
Making Use of ae Charge Informaion in MOSFET and IBT Daa Shees Ralph McArhur Senior Applicaions Engineer Advanced Power Technology 405 S.W. Columbia Sree Bend, Oregon 97702 Power MOSFETs and IBTs have
More informationMaking a Faster Cryptanalytic TimeMemory TradeOff
Making a Faser Crypanalyic TimeMemory TradeOff Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch
More informationA Reexamination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166170 (2002) Reeaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
More informationMeasuring macroeconomic volatility Applications to export revenue data, 19702005
FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a
More informationOn the degrees of irreducible factors of higher order Bernoulli polynomials
ACTA ARITHMETICA LXII.4 (1992 On he degrees of irreducible facors of higher order Bernoulli polynomials by Arnold Adelberg (Grinnell, Ia. 1. Inroducion. In his paper, we generalize he curren resuls on
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationDependent Interest and Transition Rates in Life Insurance
Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prinou should hae 1 quesions. Muliplechoice quesions may coninue on he ne column or page find all choices before making your selecion. The
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationMotion Along a Straight Line
Moion Along a Sraigh Line On Sepember 6, 993, Dave Munday, a diesel mechanic by rade, wen over he Canadian edge of Niagara Falls for he second ime, freely falling 48 m o he waer (and rocks) below. On his
More informationAP Calculus AB 2010 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College
More informationTSGRAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999
TSGRAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macrodiversiy for he PRACH Discussion/Decision
More informationApplied Intertemporal Optimization
. Applied Ineremporal Opimizaion Klaus Wälde Universiy of Mainz CESifo, Universiy of Brisol, UCL Louvain la Neuve www.waelde.com These lecure noes can freely be downloaded from www.waelde.com/aio. A prin
More informationInventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds
OPERATIONS RESEARCH Vol. 54, No. 6, November December 2006, pp. 1079 1097 issn 0030364X eissn 15265463 06 5406 1079 informs doi 10.1287/opre.1060.0338 2006 INFORMS Invenory Planning wih Forecas Updaes:
More informationARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 14, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationConceptually calculating what a 110 OTM call option should be worth if the present price of the stock is 100...
Normal (Gaussian) Disribuion Probabiliy De ensiy 0.5 0. 0.5 0. 0.05 0. 0.9 0.8 0.7 0.6? 0.5 0.4 0.3 0. 0. 0 3.6 5. 6.8 8.4 0.6 3. 4.8 6.4 8 The BlackScholes Shl Ml Moel... pricing opions an calculaing
More informationNikkei Stock Average Volatility Index Realtime Version Index Guidebook
Nikkei Sock Average Volailiy Index Realime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
More informationNiche Market or Mass Market?
Niche Marke or Mass Marke? Maxim Ivanov y McMaser Universiy July 2009 Absrac The de niion of a niche or a mass marke is based on he ranking of wo variables: he monopoly price and he produc mean value.
More informationLLC Resonant Converter Reference Design using the dspic DSC
LLC Resonan Converer Reference Design using he dspic DSC 2010 Microchip Technology Incorporaed. All Righs Reserved. LLC Resonan Converer Webinar Slide 1 Hello, and welcome o his web seminar on Microchip
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More informationPricing FixedIncome Derivaives wih he ForwardRisk Adjused Measure Jesper Lund Deparmen of Finance he Aarhus School of Business DK8 Aarhus V, Denmark Email: jel@hha.dk Homepage: www.hha.dk/~jel/ Firs
More informationDYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationModeling VIX Futures and Pricing VIX Options in the Jump Diusion Modeling
Modeling VIX Fuures and Pricing VIX Opions in he Jump Diusion Modeling Faemeh Aramian Maseruppsas i maemaisk saisik Maser hesis in Mahemaical Saisics Maseruppsas 2014:2 Maemaisk saisik April 2014 www.mah.su.se
More informationII.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal
Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.
More informationThe option pricing framework
Chaper 2 The opion pricing framework The opion markes based on swap raes or he LIBOR have become he larges fixed income markes, and caps (floors) and swapions are he mos imporan derivaives wihin hese markes.
More informationDOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR
Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios
More informationHedging with Forwards and Futures
Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buyside of a forward/fuures
More informationThe Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas
The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he
More informationOPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011ABV1 EKHBRD014ABV1 EKHBRD016ABV1
OPERAION MANUAL Indoor uni for air o waer hea pump sysem and opions EKHBRD011ABV1 EKHBRD014ABV1 EKHBRD016ABV1 EKHBRD011ABY1 EKHBRD014ABY1 EKHBRD016ABY1 EKHBRD011ACV1 EKHBRD014ACV1 EKHBRD016ACV1 EKHBRD011ACY1
More informationPATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM
PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM WILLIAM L. COOPER Deparmen of Mechanical Engineering, Universiy of Minnesoa, 111 Church Sree S.E., Minneapolis, MN 55455 billcoop@me.umn.edu
More informationWorking Paper On the timing option in a futures contract. SSE/EFI Working Paper Series in Economics and Finance, No. 619
econsor www.econsor.eu Der OpenAccessPublikaionsserver der ZBW LeibnizInformaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Biagini, Francesca;
More informationOption PutCall Parity Relations When the Underlying Security Pays Dividends
Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 22523 Opion Puall Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,
More informationC FastDealing Property Trading Game C
AGES 8+ C FasDealing Propery Trading Game C Y Collecor s Ediion Original MONOPOLY Game Rules plus Special Rules for his Ediion. CONTENTS Game board, 6 Collecible okens, 28 Tile Deed cards, 16 Wha he Deuce?
More informationGoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results:
For more informaion on geneics and on Rheumaoid Arhriis: Published work referred o in he resuls: The geneics revoluion and he assaul on rheumaoid arhriis. A review by Michael Seldin, Crisopher Amos, Ryk
More informationAnalysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer
Recen Advances in Business Managemen and Markeing Analysis of Pricing and Efficiency Conrol Sraegy beween Inerne Reailer and Convenional Reailer HYUG RAE CHO 1, SUG MOO BAE and JOG HU PARK 3 Deparmen of
More informationCredit Index Options: the noarmageddon pricing measure and the role of correlation after the subprime crisis
Second Conference on The Mahemaics of Credi Risk, Princeon May 2324, 2008 Credi Index Opions: he noarmageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo  Join work
More informationTowards IncentiveCompatible Reputation Management
Towards InceniveCompaible Repuaion Managemen Radu Jurca, Boi Falings Arificial Inelligence Laboraory Swiss Federal Insiue of Technology (EPFL) INEcublens, 115 Lausanne, Swizerland radu.jurca@epfl.ch,
More informationInformation Theoretic Evaluation of Change Prediction Models for LargeScale Software
Informaion Theoreic Evaluaion of Change Predicion Models for LargeScale Sofware Mina Askari School of Compuer Science Universiy of Waerloo Waerloo, Canada maskari@uwaerloo.ca Ric Hol School of Compuer
More informationA Bayesian framework with auxiliary particle filter for GMTI based ground vehicle tracking aided by domain knowledge
A Bayesian framework wih auxiliary paricle filer for GMTI based ground vehicle racking aided by domain knowledge Miao Yu a, Cunjia Liu a, Wenhua Chen a and Jonahon Chambers b a Deparmen of Aeronauical
More informationPrice elasticity of demand for crude oil: estimates for 23 countries
Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh
More informationMarkit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semiannual
More informationValuation of Life Insurance Contracts with Simulated Guaranteed Interest Rate
Valuaion of Life Insurance Conracs wih Simulaed uaraneed Ineres Rae Xia uo and ao Wang Deparmen of Mahemaics Royal Insiue of echnology 100 44 Sockholm Acknowledgmens During he progress of he work on his
More informationTHE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY
Complee he form in BLOCK LETTERS Provide deails on separae shees if required To Responden Address THE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY Personal Injury Claim ificaion pursuan o he Civil Law
More informationModule 3 Design for Strength. Version 2 ME, IIT Kharagpur
Module 3 Design for Srengh Lesson 2 Sress Concenraion Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress
More informationThe Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees.
The Impac of Surplus Disribuion on he Risk Exposure of Wih Profi Life Insurance Policies Including Ineres Rae Guaranees Alexander Kling 1 Insiu für Finanz und Akuarwissenschafen, Helmholzsraße 22, 89081
More informationImpact of scripless trading on business practices of Subbrokers.
Impac of scripless rading on business pracices of Subbrokers. For furher deails, please conac: Mr. T. Koshy Vice Presiden Naional Securiies Deposiory Ld. Tradeworld, 5 h Floor, Kamala Mills Compound,
More informationImpact of Human Mobility on Opportunistic Forwarding Algorithms
Impac of Human Mobiliy on Opporunisic Forwarding Algorihms Augusin Chainreau, Pan Hui, Jon Crowcrof, Chrisophe Dio, Richard Gass, and James Sco *, Universiy of Cambridge Microsof Research Thomson Research
More informationT ϕ t ds t + ψ t db t,
16 PRICING II: MARTINGALE PRICING 2. Lecure II: Pricing European Derivaives 2.1. The fundamenal pricing formula for European derivaives. We coninue working wihin he Black and Scholes model inroduced in
More informationThe Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies
1 The Ineracion of Guaranees, Surplus Disribuion, and Asse Allocaion in Wih Profi Life Insurance Policies Alexander Kling * Insiu für Finanz und Akuarwissenschafen, Helmholzsr. 22, 89081 Ulm, Germany
More informationWorking Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits
Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion
More informationDefault Risk in Equity Returns
Defaul Risk in Equiy Reurns MRI VSSLOU and YUHNG XING * BSTRCT This is he firs sudy ha uses Meron s (1974) opion pricing model o compue defaul measures for individual firms and assess he effec of defaul
More informationLIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b
LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.
More informationDoes International Trade Stabilize Exchange Rate Volatility?
Does Inernaional Trade Sabilize Exchange Rae Volailiy? HuiKuan Tseng, KunMing Chen, and ChiaChing Lin * Absrac Since he early 980s, major indusrial counries have been suffering severe mulilaeral rade
More informationThe Roos of Lisp paul graham Draf, January 18, 2002. In 1960, John McCarhy published a remarkable paper in which he did for programming somehing like wha Euclid did for geomery. 1 He showed how, given
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4112008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More informationMarkov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension
Markov Chain Modeling of Policy Holder Behavior in Life Insurance and Pension Lars Frederik Brand Henriksen 1, Jeppe Woemann Nielsen 2, Mogens Seffensen 1, and Chrisian Svensson 2 1 Deparmen of Mahemaical
More informationIMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION. Tobias Dillmann * and Jochen Ruß **
IMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS FROM OPTION PRICING TO THE PRICE OF THE OPTION Tobias Dillmann * and Jochen Ruß ** ABSTRACT Insurance conracs ofen include socalled implici or embedded opions.
More informationOptimal Monetary Policy When LumpSum Taxes Are Unavailable: A Reconsideration of the Outcomes Under Commitment and Discretion*
Opimal Moneary Policy When LumpSum Taxes Are Unavailable: A Reconsideraion of he Oucomes Under Commimen and Discreion* Marin Ellison Dep of Economics Universiy of Warwick Covenry CV4 7AL UK m.ellison@warwick.ac.uk
More informationUSE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES
USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were
More informationCALCULATION OF OMX TALLINN
CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, realime and closing value of he Index...3 3.2. Index
More informationPremium indexing in lifelong health insurance
Premium indexing in lifelong healh insurance W. Vercruysse 1, J. Dhaene 1, M. Denui 2, E. Piacco 3, K. Anonio 4 1 KU Leuven, Belgium 2 U.C.L., LouvainlaNeuve, Belgium 3 Universià di Triese, Triese, Ialy
More informationRelationship between stock index and increments of stock market trading accounts
Relaionship beween sock index and increens of sock arke rading accouns Zhenlong Zheng, Yangshu Liu Zhenlong Zheng, a professor fro Deparen of Finance, Xiaen Universiy, Xiaen, Fujian, 6005, China. Eail:
More informationDETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUNSHAN WU
Yugoslav Journal of Operaions Research 2 (22), Number, 67 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUNSHAN WU Deparmen of Bussines Adminisraion
More informationLongevity 11 Lyon 79 September 2015
Longeviy 11 Lyon 79 Sepember 2015 RISK SHARING IN LIFE INSURANCE AND PENSIONS wihin and across generaions Ragnar Norberg ISFA Universié Lyon 1/London School of Economics Email: ragnar.norberg@univlyon1.fr
More informationThe Application of Multi Shifts and Break Windows in Employees Scheduling
The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance
More informationSOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS
SOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS Noe: Two DOE Handbooks are used in conjuncion wih he pracice quesions and problems below o provide preparaory maerial for he NPS
More informationSTABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS
STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS ELLIOT ANSHELEVICH, DAVID KEMPE, AND JON KLEINBERG Absrac. In he dynamic load balancing problem, we seek o keep he job load roughly
More informationA UNIFIED APPROACH TO MATHEMATICAL OPTIMIZATION AND LAGRANGE MULTIPLIER THEORY FOR SCIENTISTS AND ENGINEERS
A UNIFIED APPROACH TO MATHEMATICAL OPTIMIZATION AND LAGRANGE MULTIPLIER THEORY FOR SCIENTISTS AND ENGINEERS RICHARD A. TAPIA Appendix E: Differeniaion in Absrac Spaces I should be no surprise ha he differeniaion
More informationACTUARIAL FUNCTIONS 1_05
ACTUARIAL FUNCTIONS _05 User Guide for MS Office 2007 or laer CONTENT Inroducion... 3 2 Insallaion procedure... 3 3 Demo Version and Acivaion... 5 4 Using formulas and synax... 7 5 Using he help... 6 Noaion...
More informationOptimal Life Insurance Purchase and Consumption/Investment under Uncertain Lifetime
Opimal Life Insurance Purchase and Consumpion/Invesmen under Uncerain Lifeime Sanley R. Pliska a,, a Dep. of Finance, Universiy of Illinois a Chicago, Chicago, IL 667, USA Jinchun Ye b b Dep. of Mahemaics,
More informationAnalysis of optimal liquidation in limit order books
Analysis of opimal liquidaion in limi order books James W. Blair, Paul V. Johnson, & Peer W. Duck Absrac In his paper we sudy he opimal rading sraegy of a passive rader who is rading in he limi order book.
More informationA Generalized Bivariate OrnsteinUhlenbeck Model for Financial Assets
A Generalized Bivariae OrnseinUhlenbeck Model for Financial Asses Romy Krämer, Mahias Richer Technische Universiä Chemniz, Fakulä für Mahemaik, 917 Chemniz, Germany Absrac In his paper, we sudy mahemaical
More informationImpact of Human Mobility on the Design of Opportunistic Forwarding Algorithms
Impac of Human Mobiliy on he Design of Opporunisic Forwarding Algorihms Augusin Chainreau, Pan Hui *, Jon Crowcrof *, Chrisophe Dio, Richard Gass, and James Sco, Thomson Research 46 quai A Le Gallo 92648
More informationOptimal Stock Selling/Buying Strategy with reference to the Ultimate Average
Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July
More informationDistributed and Secure Computation of Convex Programs over a Network of Connected Processors
DCDIS CONFERENCE GUELPH, ONTARIO, CANADA, JULY 2005 1 Disribued and Secure Compuaion of Convex Programs over a Newor of Conneced Processors Michael J. Neely Universiy of Souhern California hp://wwwrcf.usc.edu/
More informationMSCI Index Calculation Methodology
Index Mehodology MSCI Index Calculaion Mehodology Index Calculaion Mehodology for he MSCI Equiy Indices Index Mehodology MSCI Index Calculaion Mehodology Conens Conens... 2 Inroducion... 5 MSCI Equiy Indices...
More informationNew Pricing Framework: Options and Bonds
arxiv:1407.445v [qfin.pr] 14 Oc 014 New Pricing Framework: Opions and Bonds Nick Laskin TopQuark Inc. Torono, ON, M6P P Absrac A unified analyical pricing framework wih involvemen of he sho noise random
More informationSEASONAL ADJUSTMENT. 1 Introduction. 2 Methodology. 3 X11ARIMA and X12ARIMA Methods
SEASONAL ADJUSTMENT 1 Inroducion 2 Mehodology 2.1 Time Series and Is Componens 2.1.1 Seasonaliy 2.1.2 TrendCycle 2.1.3 Irregulariy 2.1.4 Trading Day and Fesival Effecs 3 X11ARIMA and X12ARIMA Mehods
More informationOptimal Consumption and Insurance: A ContinuousTime Markov Chain Approach
Opimal Consumpion and Insurance: A ConinuousTime Markov Chain Approach Holger Kraf and Mogens Seffensen Absrac Personal financial decision making plays an imporan role in modern finance. Decision problems
More information