We reconsider a formula for arbitrary moments of expected discounted dividend payments in a spectrally negative Lévy risk model that was obtained in Renaud and Zhou (2007, [4]) and in Kyprianou and Palmowski (2007, [3]) and extend the result to stationary Markov processes that are skip-free upwards.
This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale (RTS) of economic units with multiple inputs and outputs. It is frequently noticed that when we increase the input of a decision making unit (DMU) with a certain status of RTS, different status of RTS is observed. For example, when we increase the input of a DMU with constant RTS under the traditional method, a decreasing RTS is often observed instead of the expected constant RTS. We thus define the RTS of each DMU in both input expansion and contraction regions respectively. The research starts from transferring the production possibility set into the intersection form, by giving the explicit linear inequality representation of production frontiers. The RTS structural characteristics of DMUs' on the production frontier are described. Status of RTS of those DMUs on the production frontier include increasing RTS, constant RTS, decreasing RTS, saturated RTS and evidence of congestion. Necessary and sufficient conditions for RTS evaluation are provided. The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.
Let Ω ⊂ R^{n} be a bounded domain, H = L^{2}(Ω), L : D(L) ⊂ H → H be an unbounded linear operator, f ∈ C(Ω × R, R) and λ ∈ R. The paper is concerned with the existence of positive solutions for the following nonlinear eigenvalue problem
Lu = λf(x, u), u ∈ D(L),
which is the general form of nonlinear eigenvalue problems for differential equations. We obtain the global structure of positive solutions, then we apply the results to some nonlinear eigenvalue problems for a secondorder ordinary differential equation and a fourth-order beam equation, respectively. The discussion is based on the fixed point index theory in cones.
The paper studies the muiti-agent cooperative hedging problem of contingent claims in the complete market when the g-expected shortfall risks are bounded. We give the optimal cooperative hedging strategy explicitly by the Neyman-Pearson lemma under g-probability.
Bunimovich billiards are ergodic and mixing. However, if the billiard table contains very large arcs on its boundary then if there exist trajectories experience infinitely many collisions in the vicinity of periodic trajectories on the large arc. The hyperbolicity is nonuniform and the mixing rate is very slow. The corresponding dynamics are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. The study of mixing rates in intermittent chaotic systems is more difficult than that of truly chaotic ones, and the resulting estimates may depend on delicate details of the dynamics in the traps. We present a rigorous analysis of the corresponding singularities and correlations to certain class of billiards and show the mixing rate is of order 1/n.
In this paper, we study the p-Laplacian-Like equations involving Hardy potential or involving critical exponent and prove the existence of one or infinitely many nontrivial solutions. The results of the equations discussed can be applied to a variety of different fields in applied mechanics.
In this paper, we investigate the existence of incomplete group divisible designs (IGDDs) with block size four, group-type (g, h)^{u} and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg(u-1) ≡ 0 (mod 3), λ(g-h)(u-1) ≡ 0 (mod 3), and λu(u-1)(g^{2}-h^{2}) ≡ 0 (mod 12). These necessary conditions are shown to be sufficient for all λ ≥ 2. The known existence result for λ = 1 is also improved.
In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter
where λ > 0 is a parameter, 0 < ξ1 < ξ2 < · · · < ξm-2 < 1 with 0 < and f(t, u) ≥ -M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.
By using the continuation theorem of Mawhin's coincidence degree theory and the Liapunov functional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.
A new expression is established for the common solution to six classical linear quaternion matrix equations A_{1}X = C_{1}, XB_{1} = C_{3}, A_{2}X = C_{2}, XB_{2} = C_{4}, A_{3}XB_{3} = C_{5}, A_{4}XB_{4} = C_{6} which was investigated recently by Wang, Chang and Ning (Q. Wang, H. Chang, Q. Ning, The common solution to six quaternion matrix equations with applications, Appl. Math. Comput. 195: 721-732 (2008)). Formulas are derived for the maximal and minimal ranks of the common solution to this system. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition is presented for the invariance of the rank of the general solution to this system. Some known results can be regarded as the special cases of the results in this paper.
By using some results of pseudo-monotone operator, we discuss the existence and uniqueness of the solution of one kind nonlinear Neumann boundary value problems involving the p-Laplacian operator. We also construct an iterative scheme converging strongly to this solution.
Let A be a function with derivatives of order m and D^{ γ}A ∈ _{β} (0 < β < 1, |γ| = m). The authors in the paper prove that if Ω(x, z) ∈ L^{∞}(R^{n}) × L^{s}(S^{n-1}) (s ≥ n/(n-β)) is homogenous of degree zero and satisfies the mean value zero condition about the variable z, then both the generalized commutator for Marcinkiewicz type integral μ_{Ω}^{A} and its variation are bounded from L^{p}(R^{n}) to L^{q}(R^{n}), where 1 < p < n/β and 1/q = 1/p-β/n. The authors also consider the boundedness of μ_{Ω}^{A} and its variation on Hardy spaces.
A combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem which includes molecular diffusion and dispersion in porous media is investigated. That is to say, the mixed finite element method with Raviart-Thomas space is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin (SIPG) approximation. Based on projection interpolations and induction hypotheses, a superconvergence estimate is obtained. During the analysis, an extension of the Darcy velocity along the Gauss line is also used in the evaluation of the coefficients in the Galerkin procedure for the concentration.
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(Δt + h^{k+1} + H^{2k+2-d/2}) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value one. Let {1, r_{2}, · · · , r_{N}} be the eigenvalues of stochastic matrix X of size N × N. We will present in this paper a simple necessary and sufficient condition for X such that |r_{j}| < 1, j = 2, · · ·,N. Moreover, such condition can be very quickly examined by using some search algorithms from graph theory.
In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation (MSE) and mean absolute estimation (MAE) criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.
Let G be a graph of maximum degree at most four. By using the overlap matrix method which is introduced by B. Mohar, we show that the average genus of G is not less than (1/3) of its maximum genus, and the bound is best possible. Also, a new lower bound of average genus in terms of girth is derived.
This paper considers the optimal control problem with constraints for an insurance company. The risk process is assumed to be a jump-diffusion process and the risk can be reduced through an excess of loss (XL) reinsurance. In addition, the surplus can be invested in the financial market. In the financial market, the short-selling constraint is one of the main factors which make models more realistic. Our goal is to find the optimal investment-reinsurance policy without short-selling, which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton-Jacobi-Bellman equation, the value function and the optimal investment-reinsurance policy are given in a closed form.
In this paper, by analyzing the propositions of solution of the convex quadratic programming with nonnegative constraints, we propose a feasible decomposition method for constrained equations. Under mild conditions, the global convergence can be obtained. The method is applied to the complementary problems. Numerical results are also given to show the efficiency of the proposed method.
Let N = (G, c) be a random electrical network obtained by assigning a certain resistance for each edge in a random graph G ∈ G(n, p) and the potentials on the boundary vertices. In this paper, we prove that with high probability the potential distribution of all vertices of G is very close to a constant.