periodic payments of interest with lump sum principal payment

... the log difference of GDP The inflation series is based on the seasonally adjusted harmonised index of consumer prices spliced with the retail prices index excluding mortgage payments This data ... diagonal elements of the Cholesky decomposition of vols The prior for the off-diagonal elements At is ˆ A0 ∼ N aols ,V aols ˆ ˆ where aols are the off-diagonal elements of vols , with each row ˆ ... mean of the non-zeros ˜ ˆ ˆ elements of A, M denotes the posterior mean of the variance-covariance of τt , G Working Paper No 450 May 2012 39 ˆ ˜ denotes the posterior mean of the variance of νt...

Ngày tải lên: 06/03/2014, 14:20

... definition of triple systems in [4] and our definition Hence the proofs of the following results are completely analogous to the proofs in [4] The description of the focal manifolds by means of the ... complete our proof of Theorem 1.1 by means of the following Lemma 4.1 Let M be an isoparametric hypersurface with four distinct principal curvatures in the unit sphere S2l−1 of the Euclidean ... injective for every A ∈ A(M+ )\{0} Without loss of generality we may assume that A = (aij )i,j is a diagonal matrix with aii = for i > t, where t denotes the rank of A Assume that there exists a matrix...

Ngày tải lên: 22/03/2014, 20:21

... trình bày với recall versus 1-precision: • Ở # correspondences viết tắt cho the ground truth number of matching regions between the images • Các đường cong thu cách thay đổi khoảng ngưỡng mô tả hoàn...

Ngày tải lên: 13/05/2014, 21:14

... http://www.boundaryvalueproblems.com/content/2011/1/8 Page of Proof Let u Î K, then in case of g = +∞, since G(t, s) ≥ 0, we have Lu(t) ≥ on [0, T]; in case of g r2 and f∞ < r2 in case of g = +∞ Then problem (2) has at least one positive solution Proof Since f0 > r2, there...

Ngày tải lên: 21/06/2014, 01:20

... costs of firms, as well as consumer preferences This is typical in the field of insurance Expected costs of medical insurance, for example, depend on the health characteristics of the insured Of course, ... is assumed that the unit costs of good i consumed by individuals with a given α (type α) is ci (α) Health and longevity insurance are leading examples of this situation The health status of an ... amount of annuities, z is expected lifetime, b is the amount of life insurance (=bequests), and y is the amount of the numeraire Utility of consumption, u, and the utility from bequests, v, are assumed...

Ngày tải lên: 21/06/2014, 08:20

... Maximization of expected utility for ≤ z ≤ M yields constant consumption, denoted c, whose level depends, of course, on the expected level of annuities held at age M, F (M)a(M) This level of annuities, ... ≤ z ≤ T Let c(z) be consumption at age z, ≤ z ≤ M, and ci (z) be consumption at age z, M ≤ z ≤ T, of a risk-class-i (state-i) individual, i = 1, Similarly, Ri is the age of retirement in state ... p)z2 ≤ β ≤ This is an important result: In the first best, optimum consumption and age of retirement are independent of the state of nature This is equivalent, as we shall demonstrate, to full insurance...

Ngày tải lên: 21/06/2014, 08:20

... retirement provided consumption is constant, but it also raises consumption, thereby decreasing the marginal utility of consumption and hence the value of this postponement Which of these opposite ... is a positive rate of interest on assets, the competitive rate of return on annuities is equal to the rate of interest plus the hazard rate The reason is obvious: The issuers of annuities can invest ... to shift consumption to early ages Consequently, the benefits of a marginal postponement of retirement are larger if retirement is contemplated at a relatively old age (with low consumption and...

Ngày tải lên: 21/06/2014, 08:20

... expansion of investment options: Starting with diversified common stock portfolios, policies now offer a variety of specialized portfolios of bonds and securities With the exception of the United ... provide not only a flow of income during life but also payment of a lump sum to a designated beneficiary if death occurs soon after annuitization The optimum allocation of resources between annuities ... vary with age If individuals are planning for rising or declining consumption with age, it can be expected that the market will provide annuities with a payout profile that matches these consumption...

Ngày tải lên: 21/06/2014, 08:20

... or not to leave: The distribution of bequest motives, National Bureau of Economic Research, Working Paper No 11767 Kotlikoff, L., and L Summers 1981 The role of intergenerational transfers in ... economics of incomplete information Quarterly Journal of Economics 90: 624–649 Salanie, B 2000 Microeconomics of Market Failure Cambridge, MA: MIT Press Salanie, B 2003 The Economics of Taxation ... bequests and, 82; bundling and, 131; defined, 67; empirical importance of, 67; general model for, 69–71; proof of, 76; rate of return and, 71; refundable annuities and, 144–49; risk class and,...

Ngày tải lên: 21/06/2014, 08:20

... families of generalized quasipseudodistances and define three new kinds of dissipative set-valued dynamic systems with these families of generalized quasipseudodistances and with some families of not ... ⊂ SJ;T x } Convergence of Dynamic Processes and Generalized Sequences of Iterations and Periodic Points of Dissipative Set-Valued Dynamic Systems in Quasigauge Spaces with Generalized Quasipseudodistances ... diagonal of X×X and, for each M ⊂ X×X, M2 { x, y ∈ X × X : ∃z∈X { x, z ∈ M ∧ z, y ∈ M}} The elements of U are called entourages or vicinities ii A subfamily B of U is called a base of the quasiuniformity...

Ngày tải lên: 21/06/2014, 11:20

... developments of the secondorder systems 1.1 , see In this paper, we use this kind of condition to consider the existence of periodic solutions of first-order linear Hamiltonian system with a nonlinear ... In the proof of 2.2 , we use the imbedding result 1.10 , the finite dimensionality of E , and Young inequality In the proof of 2π |un |α |un | dt ≤ un C un 2α 2.4 , we need a little bit of caution ... ∞, by condition G This completes the proof Proof of Theorem 1.2 We still use Theorem 2.1 and only consider the case where G holds Under the assumption of the theorem, E0 We set E E1 ⊕ E2 : E...

Ngày tải lên: 21/06/2014, 18:20

... containment of almost periodic solution of equation x t px t − qx t f t was studied in 9, 10 Up to now, there have been no papers concerning the spectrum containment of almost periodic solution of equation ... solution of 1.1 , then x t px t − are continuous at t ∈ R, which guarantees the uniqueness of solution of 1.1 and cannot be omitted To study the spectrum of almost periodic solution of 1.1 , ... Λf {kπ : k ∈ Z} holds, where the sum of sets A and B is defined as A B {a b : a ∈ A, b ∈ B} We postpone the proof of this theorem to the next section The Proof of Main Theorem To show the Main...

Ngày tải lên: 21/06/2014, 20:20

... solution z n of G such that z0 s ∈ K for s ≤ 0, by the same argument for Σ-calculations with condition of Ki as in the proof of Lemma 2.2 Then, the same argument as in the proof of Lemma 2.2 ... Existence of Periodic Solutions and Almost Periodic Solutions, vol 14 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1975 Y Song and H Tian, Periodic and almost periodic solutions of ... -translation number of f n, x In order to formulate a property of almost periodic functions, which is equivalent to the above difinition, we discuss the concept of the normality of almost periodic functions...

Ngày tải lên: 21/06/2014, 20:20

... image of the PMO NFs (as-synthesized) ordered arrangement of the mesopores investigated by SAXS confirms periodicity of mesopores in the organosilica NFs The N2 adsorption–desorption isotherm of ... (Fig 4b) along with the HRTEM image confirms the periodicity of the mesopores in the NR sample The NRs have a type-IV N2 adsorption–desorption isotherm (Fig 5b) with a BET surface area of 936 m2 g-1 ... further confirm the absence of the template and the presence of the organic groups The sample has a typeIV isotherm with a BET surface area of 815 m2 g-1 and pore volume of 0.827 cm3 g-1 The BJH...

Ngày tải lên: 22/06/2014, 00:20

... result than that of Theorem 3.2, that is, under the assumption of asymptotic almost periodicity of a bounded solution of 2.7 , he showed the existence of an almost periodic solution of the limiting ... induced topology by ρ is the same as the topology of convergence on any finite subset of Z− In view of almost periodicity, for any sequence nk ⊂ Z with nk → ∞ as k → ∞, there exists a subsequence ... analogue of Hamaya’s definition in 2.14 S K Choi and N Koo Main results Definition 3.1 see A function φ : Z → Rn is called asymptotically almost periodic if it is a sum of an almost periodic...

Ngày tải lên: 22/06/2014, 11:20

... existence of a unique nontrivial periodic solution to a class of equations of Li´nard’s type, Journal of Differential Equae tions 46 (1982), no 3, 356–378 [12] P N Savel’ev, Dissipativity of the ... multiplicity results for periodic solutions of semilinear Duffing equations, Journal of Differential Equations 105 (1993), no 2, 364–409 [5] C Fabry and D Fayyad, Periodic solutions of second order differential ... Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like a operators, Journal of Differential Equations 145 (1998), no 2, 367–393 [9] J Mawhin and J R Ward Jr., Periodic solutions of...

Ngày tải lên: 22/06/2014, 22:20

... proof of Theorem 3.4, we can show that { p(n)} is an ω -periodic solution of (3.1) Almost periodic systems In this section, we discuss the existence of asymptotically almost periodic solutions of ... {x(n)}n≥n0 is any solution of (2.6) Periodic systems In this section, we discuss the existence of periodic solutions of (2.6), namely, x(n + 1) = F n,xn , n ≥ 0, (3.1) under a periodic condition (H3) ... {u(n)}n≥0 of (3.1) is ᐁᏭ᏿, then system (3.1) has a periodic solution of period mω for some positive integer m, which is also ᐁᏭ᏿ Proof Set uk (n) = u(n + kω), k = 1,2, By the proof of Theorem...

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 05/08/2014, 15:21

... = y By the 1-periodicity of f , this shows that u can be extended to a 1 -periodic mild solution of Eq (1) The uniqueness of such 1 -periodic solutions follows from the uniqueness of the element ... t)u(t)dt The notion of Beurling spectrum of a function u ∈ BU C(R, X) coincides with the one of Carleman spectrum, which consists of all ξ ∈ R such that the Carleman– Fourier transform of u, defined ... on the asymptotic behavior of solutions of ill-posed equations associated with C-semigroups The existence of almost periodic solutions to ill-posed evolution equations of the form (1) has not been...

Ngày tải lên: 06/08/2014, 05:20

... sequence of symbols If v and w are words, then vw is the concatenation and w k is the concatenation of k copies of w The length |w| of w is the number of symbols in the sequence The descent word of ... length of the ith run in α The size L of a run word L is the sum of its parts plus Thus, its size is one more than the length of the corresponding descent word In other words, it is the size of the ... is the solution of MD = such that φ(x, µ) dx = The value of φ(y, µR ) is found by replacing x with y and µ with µR The values of λ and |r| are the same for µ and µR We may assume arg r = if...

Ngày tải lên: 07/08/2014, 08:20