hamiltonian in quantum mechanics

... The starting point for the application of path integrals and Hamiltonians in finance is in stock option pricing Path integrals are subsequently applied to the modelling of linear and nonlinear theories ... market information The in ow of new information comes in randomly – in bits and pieces – causing random responses from the market players, due to the incomplete nature of the incoming information, ... partially hedged instrument Hedging is analogous to buying insurance The cost of hedging is the transaction costs incurred in buying and selling the needed securities – and, similar to insurance, is...

Ngày tải lên: 23/03/2014, 12:20

... together in this discipline in order to incorpor a te the use of advanced mathe m a tics with everyday finance (Stix, 1998) Although financial engineering deals with many aspects of finance, the main ... criticism A New Breed of $cience In recent years, a new discipline called financial engineering has emerged in order to attem p t to under s t a n d finance using a scientific appro ac h Mathema ... Colorad oa n upset winnings We minimize risk at the cost of lowering our possible However, since Detroit is favored, the chances of winning $5 are substan tial A more busines s - oriente d example...

Ngày tải lên: 08/04/2014, 12:09

... scenarios from this viewpoint (b) b = 2|m| + corresponds to a quantum number In the physical setting, we can only have b ∈ N In this integer case, we only obtain one (linearly independent) power series ... nevertheless it is interesting for quantum mechanics because of the energy quantization in (c) Maybe something similar can be obtained if d = 0—probably via perturbation methods (One has to take into consideration ... recovering the following Bessel-like equation for the wave function ψ: x2 ψ + xψ + − a2 a(b + 1) (b − 1)2 x + c− x + dx − ψ = 4 (2.3) (In detail, (2.3) is either obtained by inserting the “undoing”...

Ngày tải lên: 23/06/2014, 00:20

... PHÁI SINH 1: Khái niệm phân loại chứng khoán phái sinh 1.1 : Khái niệm : Chứng khoán phái sinh công cụ tài mà giá trị phụ thuộc vào giá trị chứng khoán sở khác Như vậy,chứng khoán phái sinh hiểu ... giá cổ phiếu trở thành nhu cầu thiết yếu quan trọng b.Giá trị lý thuyết (intrinsic value ) : Giá trị lý thuyết (intrinsic value ) chứng khoán giá trị mà chứng khoán dó nên có dựa yếu tố có liên ... tồn a.Thiếu thông tin Thiếu thông tin vấn đề làm cho thị trường chứng khoán sức hấp dẫn nhà đầu tư.Việc thiếu thông tin ảnh hưởng tới phương pháp định sau Thiếu thông tin thống kê thị trường:Hoạt...

Ngày tải lên: 09/04/2013, 15:03

... x = erT ,tuxxt; x: 186 Plugging these formulas into the partial differential equation for v and cancelling the erT ,t appearing in every term, we obtain the Black-Scholes partial differential ... 0;   be an initial condition for the SDE (5.1) We simplify notation by writing IE rather than IE 0; Theorem 5.50 Starting at X 0 =  , the process v t; X t satisfies the martingale property: ... from time to time t0 , and based on this information, you want to estimate hX t1, the only relevant information is the value of X t0 You imagine starting the SDE  at time t0 at value X t0,...

Ngày tải lên: 18/10/2013, 03:20

... singularity in our original (t, r, θ, φ) system In the Eddington-Finkelstein coordinates the condition for radial null curves is solved by d˜ u = dr 0, 1− 2GM r −1 (infalling) (outgoing) (7.71) ... be to move in the potential until it reaches a “turning point” where V (r) = E , where it will begin moving in the other direction Sometimes there may be no turning point to hit, in which case ... outgoing ˜ ones satisfy v = constant Now consider going back to the original radial coordinate r, ˜ but replacing the timelike coordinate t with the new coordinate u These are known as ˜ Eddington-Finkelstein...

Ngày tải lên: 23/10/2013, 20:20

... adding or subtracting 0.0816 to give the remaining values The stock price values in the second column are obtained simply by taking exponentials of the first column Note that the S values in this ... at all A comparison of the methods is given in Section 8.5 (iv) The interesting discretization methods laid out in Section 8.1 can be combined into a single formula: n+1 ˆ u n+1 − u n = α δx θu ... are explained below; but before turning to these, it is worth pointing out to the reader that the numerical solution of partial differential equations is something of an art form, containing many...

Ngày tải lên: 25/10/2013, 19:20

... practical for hedging, but a direct investment in the underlying index is often not possible since no traded instrument exists In compensation, the futures markets on most major stock indices are very ... The Black Scholes Model (v) Stock Indices and Commodities: In theory one can invest in a stock index by buying a prescribed number of shares of each stock in the index This is obviously too cumbersome ... replaced by the foreign currency interest rate This is a particularly easy substitution to make since interest rates are incurred continuously In fact the continuous dividend yield Black Scholes...

Ngày tải lên: 25/10/2013, 19:20

... tX l i s sinh bi tt c cỏc bin ngu nhiờn X s vi s t , tc l tX = ( X s , s t ) (nú phn ỏnh nhng thụng tin v din bin quỏ kh ca quỏ trỡnh X cho n thi im t) Ta gi tX l trng thụng tin v X 1.1.9 ... thc hin ti trng i Hc Vinh di s hng dn tn tỡnh ca TS Nguyn Huy Chiờu Tỏc gi xin c by t lũng bit n sõu sc n Thy, ngi ó ch bo, giỳp tỏc gi sut quỏ trỡnh thc hin ti ny Nhõn dp ny tỏc gi cng xin gi ... c hỡnh thnh v phỏt trin hn 10 nm, th trng chng khoỏn Vit Nam cha cú cỏc sn phm phỏi sinh ti chớnh S bin ng ln ca VN-Index ang t yờu cu cp bỏch phi hỡnh thnh th trng phỏi sinh ti chớnh, nhm hn...

Ngày tải lên: 19/12/2013, 14:05

... động ngẫu nhiên phát triển theo phân phối logarit chuẩn Lãi suất phi rủi ro độ bất ổn tỷ suất sinh lợi theo logarit cổ phiếu khơng thay đổi suốt thời gian đáo hạn quyền chọn Khơng có thuế chi ... N(d1), N(d2) = xác suất phân phối chuẩn tích lũy σ = độ bất ổn hàng năm (độ lệch chuẩn) tỷ suất sinh lợi ghép lãi liên tục (logarit) cổ phiếu lãi suất phi rủi ro ghép lãi liên tục CÔNG THỨC ĐOẠT...

Ngày tải lên: 25/01/2014, 11:20

... occur in a wide range of questions, in both pure and applied mathematics They appear in linear and nonlinear PDEs that arise, for example, in differential geometry, harmonic analysis, engineering, ... Recall that in general, a pointwise limit of continuous maps need not be continuous The linearity assumption plays an essential role in Theorem 2.2 Note, however, that in the setting of Theorem ... in the case that inf x∈K x − x0 is not achieved (see, e.g., Exercise 1.17) The theory of minimal surfaces provides an interesting setting in which the primal problem (i.e., inf x∈E {ϕ(x) + ψ(x)})...

Ngày tải lên: 04/02/2014, 11:10

... found by inspecting the given inhomogeneity The table compresses several cases For instance, f (t) in line is a polynomial if α = or an exponential if n = and α = In line 2, both sine and cosine must ... by deriving the mathematical model in a number of cases, by using physical reasoning in the mathematical development, by interpreting mathematical results in physical terms, and by studying the ... conditions 0.4 Singular Boundary Value Problems A boundary value problem can be singular in two different ways In one case, an endpoint of the interval of interest is a singular point of the differential...

Ngày tải lên: 17/02/2014, 14:20

... in nitesimal heating” and m Pk dXk as in nitesimal k=1 working” for a process In this chapter however there is no notion whatsoever of anything changing in time: everything is in equilibrium Terminology ... unifying themes: (i) the use of entropy in deriving various physical PDE, (ii) the use of entropy to characterize irreversibility in PDE evolving in time, and (iii) the use of entropy in providing ... References INTRODUCTION A Overview This course surveys various uses of “entropy” concepts in the study of PDE, both linear and nonlinear We will begin in Chapters I–III with a recounting of entropy in...

Ngày tải lên: 17/03/2014, 14:29

... discussed in Chapter References 1] E M Stein: Singular integral and di erentiability properties of functions, Princeton University Press 1970 2] B.E.J Dahlberg: Harmonic functions in Lipschitz domains, ... Zygmund: On the existence of certain singular integrals, Acta Math 88 (1952) pp 85-139 2] E M Stein: Singular integrals and di erentiability properties of functions Princeton University Press 1970 ... Cauchy integral Preprint 4: A P Calder n: Commutators, singular integral on Lipschitz curves and applications Proc of the I C M Helsinki (1978) 5: F John: Quasi-Isometric Mappings Semineri 1962-1963...

Ngày tải lên: 31/03/2014, 15:16

... unique elements or members Set elements commonly include: Ⅲ Points on a line Ⅲ Instants in time Ⅲ Coordinates in a plane Ⅲ Coordinates in space Ⅲ Coordinates on a display Ⅲ Curves on a graph or display ... point corresponding to In general, to illustrate a ϩ b ϭ c, start at the point corresponding to a, then move to the right b units, ending up at the point corresponding to c Figure 1.2 The integers ... solution for x in place of x in the second equation, obtaining: a2(Ϫb1 y Ϫ c1)/a1 ϩ b2 y ϩ c2 ϭ Solve this single-variable equation for y, using the previously outlined rules for solving single-variable...

Ngày tải lên: 31/03/2014, 16:19

... equations were investigated in [17-20] A local Hyers-Ulam stability of Jensen’s equation In 1998, Jung [16] investigated the Hyers-Ulam stability for Jensen’s equation on a restricted domain In this ... sequence in Y for all x Î X Since (Y, N) is 2n f (2n x) } converges to a point T(x) Î Y Thus, we can define a mapping T : 2n f (2n x) X ® Y by T(x) := N − limn→∞ Moreover, if we put m = in (2.11), ... real numbers t, s Letting y = x and t = s in (2.8), we infer that N f (2x) − f (x), t ≥ N (10δz0 , t) (2:9) for all x Î X and positive real number t replacing x by 2nx in (2.9), we get N f (2n+1...

Ngày tải lên: 20/06/2014, 22:20

... vinf t inf u t : u upper solution of 1.1 , u ≤ g a.e , t ∈ I 2.15 ∗ Theorem in implies that also vinf is the least Carath´ odory solution of 1.1 , thus u∗ e inf ∗ ∗ vinf ≤ U on I Hence uinf uinf ... concerns the possibility of allowing jumps in their graphs Since the task of finding a pair of lower and upper solutions is by no means easy in general, and bearing in mind that constant lower and ... actually asserts that u∗ , as defined in 2.8 , is the least inf uinf , as defined in 2.2 Carath´ odory solution, but it is easy to prove that in that case u∗ e inf Indeed, let U be an arbitrary upper...

Ngày tải lên: 21/06/2014, 20:20

... stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol 72, no 2, pp 297–300, 1978 Z Gajda, “On stability of additive mappings,” International Journal ... function f at the point x, that is, l− f x by the usual pointwise ordering of functions, that is, F ≤ G if and only if F t ≤ G t for all t in R The maximal element for Δ in this order is the ... see 20 A mapping T : 0, × 0, → 0, is a continuous triangular norm briefly, a continuous t-norm if T satisfies the following conditions: a T is commutative and associative; b T is continuous; c T...

Ngày tải lên: 22/06/2014, 02:20

... comparison principle for the Dirichlet problem for the nonlinear parabolic equation ut = Δum − buβ (1) posed in a noncylindrical space-time domain, reducing to a single point both at the initial and ... to homogeo neous Dirichlet conditions In the paper, particular care is put in considering limit situations (e.g., for the parameters involved) or in giving simpler proofs for standard situations ... operators, showing that some properties are typical of elliptic equations per se, nothwithstanding their kind Before coming to the full proof of the main result, a nice sketch of the main ideas is...

Ngày tải lên: 22/06/2014, 19:20

... complete in P in the sense that all well-ordered and inversely well-ordered chains of U have supremums and in mums in P Proof (a) In both cases (A) and (B), the mapping x → x+ is continuous in E ... C(J,E), and there is an increasing sequence (un ) in W which converges pointwise strongly in case (A) and weakly in the case (B) to u Moreover, in both cases, u(t) ≤ liminf un (t) ≤ w(t), n→∞ t ∈ ... (2.1) of P If W is an inversely well-ordered chain in U, then −W is a well-ordered chain in −U The above proof ensures that v = sup(−W) exists in C(J,E) and belongs to P Thus, inf W = −v exists and...

Ngày tải lên: 23/06/2014, 00:20