Based on the framework of[7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump (JCIR++), and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and C^{A,B} copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and C^{A,B} copulas show that our method performs better both in computation speed and accuracy.
In this paper, some new concepts for hypergraphs are introduced. Based on the previous results, we do further research on cycle structures of hypergraphs and construct a more strictly complete cycle structure system of hypergraphs.
Let f:M → M be a partially hyperbolic diffeomorphism on a closed Riemannian manifold with uniformly compact center foliation. We show that if the center foliation of f is of dimension one then the topological entropy is constant on a small C^{1} neighborhood of f.
In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained minimization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the stability center is updated, some points in the bundle will be substituted by new ones which have lower objective values and/or constraint values, aiming at getting a better bundle. The method generates feasible serious iterates on which the objective function is monotonically decreasing. Global convergence of the algorithm is established, and some preliminary numerical results show that our method performs better than the standard feasible point bundle method.
In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.
Let Γ denote the folded (2D + 1)-cube with vertex set X and diameter D ≥ 3. Fix x ∈ X. We first define a partial order ≤ on X as follows. For y, z ∈ X let y ≤ z whenever ∂(x, y) + ∂(y, z)=∂(x, z). Let R (resp. L) denote the raising matrix (resp. lowering matrix) of Γ. Next we show that there exists a certain linear dependency among RL^{2}, LRL, L^{2}R and L for each given Q-polynomial structure of Γ. Finally, we determine whether the above linear dependency structure gives this poset a uniform structure or strongly uniform structure.
Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our Gohberg-Semencul type formula leads to an efficient way to solve the conjugate-Toeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugate-Hankel matrix is also considered.
In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painlevé-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painlevé-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.
Experiments show that the liquid helium-4 has either superfluid phase or solid phase when temperature decreases or the pressure of the system changes. In this paper, we discuss the equations which govern these phase transitions and derive the criterions for these phase changes. Meanwhile, we give related approximate solutions and draw the phase diagram. In addition, we also prove that the liquid helium-4 bifurcates from the trivial solution to an attractor as parameters cross certain critical value. The topological structure of the bifurcated attractor is also illustrated.
In this paper, we first prove that, for a non-zero function f∈D(R^{n}), its multi-Hilbert transform H_{n}f is bounded and does not have compact support. In addition, a new distribution space D'_{H} (R^{n}) is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D'_{H} (R^{n}) is the biggest subspace of D'(R^{n}) on which the extended multi-Hilbert transform is a homeomorphism.
Let G be a graph, and g, f:V (G) → Z^{+} with g(x) ≤ f(x) for each x ∈ V (G). We say that G admits all fractional (g, f)-factors if G contains an fractional r-factor for every r:V (G) → Z^{+} with g(x) ≤ r(x) ≤ f(x) for any x ∈ V (G). Let H be a subgraph of G. We say that G has all fractional (g, f)-factors excluding H if for every r:V (G) → Z^{+} with g(x) ≤ r(x) ≤ f(x) for all x ∈ V (G), G has a fractional r-factor F_{h} such that E(H) ∩ E(F_{h})=ø, where h:E(G) →[0, 1] is a function. In this paper, we show a characterization for the existence of all fractional (g, f)-factors excluding H and obtain two sufficient conditions for a graph to have all fractional (g, f)-factors excluding H.
Making use of the traditional Caputo derivative and the newly introduced Caputo-Fabrizio derivative with fractional order and no singular kernel, we extent the nonlinear Kaup-Kupershmidt to the span of fractional calculus. In the analysis, different methods of fixed-point theorem together with the concept of piccard L-stability are used, allowing us to present the existence and uniqueness of the exact solution to models with both versions of derivatives. Finally, we present techniques to perform some numerical simulations for both non-linear models and graphical simulations are provided for values of the order α=1.00; 0.90. Solutions are shown to behave similarly to the standard well-known traveling wave solution of Kaup-Kupershmidt equation.
A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. A plane graph with near-independent crossings or independent crossings, say NIC-planar graph or IC-planar graph, is a 1-planar graph with the restriction that for any two crossings the four crossed edges are incident with at most one common vertex or no common vertices, respectively. In this paper, we prove that each 1-planar graph, NIC-planar graph or IC-planar graph with maximum degree △ at least 15, 13 or 12 has an equitable △-coloring, respectively. This verifies the well-known Chen-Lih-Wu Conjecture for three classes of 1-planar graphs and improves some known results.
This paper is aimed at investigating the transient losses in the M/M/1/1 Erlang loss system. We evaluate the explicit form of the probability distribution of the number of losses in the time interval[0, t) and provide two alternative representations:one based on the iterated derivatives of hyperbolic sinus and cosine and the other on the spherical modified Bessel function of the second kind. The mathematical structures of the transient loss rate and of the transient probability of losing all customers are described and several analytical properties are derived.
In this paper, we determine the neighbor connectivity κ_{NB} of two kinds of Cayley graphs:alternating group networks AN_{n} and star graphs S_{n}; and give the exact values of edge neighbor connectivity λ_{NB} of AN_{n} and Cayley graphs generated by transposition trees Γ_{n}. Those are κ_{NB}(AN_{n})=n-1, λ_{NB}(AN_{n})=n-2 and κ_{NB}(S_{n})=λ_{NB}(Γ_{n})=n-1.
In this paper, we consider an initial boundary value problem for a 2D model of electro-kinetic fluid in a smooth and bounded domain. We prove that the model has a unique global-in-time smooth solution.
This paper investigates a fluid model driven by an M/M/1 queue with working vacations and RCE (Removal of customer in the end) policy of negative customer. In the external environment, the negative customer is not served by the server and only removes the positive customer in the end one-to-one. We establish a fluid flow model based on this stochastic process, and obtain the mean buffer content and the probability of empty buffer for this fluid queue using the LT (Laplace transform) method. Moreover, several special cases of the model here are obtained. Finally, some numerical examples are presented to demonstrate the effects of parameters on the performance indices of the fluid model.
In this paper we mainly study the difference of the weak solutions generated by a wave front tracking algorithm for the steady adiabatic Chaplygin gas dynamic system and the steady irrotational system. Under the hypothesis that the initial data are of sufficiently small total variation, we prove that the difference between the solutions to these two systems can be bounded by the cube of the total variation of the initial perturbation.
The new coupled KdV equation proposed by Ohta and Hirota, in which the phase shift depends on the mutual positions of solitons at the initial time, is investigated in the framework of prolongation structure theory. Its Lax representation is constructed.
In this paper, the existence of a nontrivial solution for a class of quasilinear elliptic equations with a disturbance term in a weighted Sobolev space is proved. The proofs rely on Galerkin method, Brouwer's theorem and a new weighted compact Sobolev-type embedding theorem established by V.L. Shapiro.