In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.
Let G be a connected graph of order n. The rainbow connection number rc(G) of G was introduced by Chartrand et al. Chandran et al. used the minimum degree δ of G and obtained an upper bound that rc(G)≤3n/(δ+1)+3, which is tight up to additive factors. In this paper, we use the minimum degree-sum σ_{2} of G to obtain a better bound rc(G) ≤(6n/(σ_{2}+2)) +8, especially when δ is small (constant) but σ_{2} is large (linear in n).
A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation times using a Markov-based approach, we are able to analyze this model as a level-dependent quasi-birth-and-death (LDQBD) process which makes the model algorithmically tractable. Several performance measures such as the stationary probability distribution and the expected number of customers in the orbit have been discussed with two different policies: deterministic time-controlled system and random time-controlled system. To give a comparison with the known vacation policy in the literature, we present the exhaustive vacation policy as a contrast between these policies under the early arrival system (EAS) and the late arrival system with delayed access (LAS-DA). Significant difference between EAS and LAS-DA is illustrated by some numerical examples.
Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Lévy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy (also called refraction strategy) forms an optimal strategy under the condition that the Lévy measure has a completely monotone density.
An extension of the invariance principle for a class of discontinuous righthand sides systems with parameter variation in the Filippov sense is proposed. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the discontinuous system to be positive on some sets. The uniform estimates of attractors and basin of attractions with respect to parameters are also obtained. To this end, we use locally Lipschitz continuous and regular Lyapunov functions, as well as Filippov theory. The obtained results settled in the general context of differential inclusions, and through a uniform version of the LaSalle invariance principle. An illustrative example shows the potential of the theoretical results in providing information on the asymptotic behavior of discontinuous systems.
We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.
The probability hypothesis density (PHD) propagates the posterior intensity in place of the poste-rior probability density of the multi-target state. The cardinalized PHD (CPHD) recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo (SMC) implementations of PHD and CPHD filters (also known as SMC-PHD and SMC-CPHD filters, respectively) for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simulation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.
This paper investigates the number of rooted unicursal planar maps and presents some formulae for such maps with four parameters: the numbers of nonrooted vertices and inner faces and the valencies of two odd vertices.
Recently, Kundu and Gupta (Metrika, 48: 83 C 97, 1998) established the asymptotic normality of the least squares estimators in the two dimensional cosine model. In this paper, we give the approximation to the general least squares estimators by using random weights which is called the Bayesian bootstrap or the random weighting method by Rubin (Annals of Statistics, 9: 130 C 134, 1981) and Zheng (Acta Math. Appl. Sinica (in Chinese), 10(2): 247 C 253, 1987). A simulation study shows that this approximation works very well.
A k-edge-coloring f of a connected graph G is a (λ_{1}, λ_{2}, …,λ_{β})-defected k-edge-coloring if there is a smallest integer β with 1≤β≤k-1 such that the multiplicity of each color j∈{1, 2, …, β} appearing at a vertex is equal to λ_{j}≥2, and each color of {β + 1, β+ 2.…, k} appears at some vertices at most one time. The (λ_{1}, λ_{2}, …,λ_{β})-defected chromatic index of G, denoted as x'(λ_{1}, λ_{2}, …,λ_{β};G), is the smallest number such that every (λ_{1}, λ_{2}, …,λ_{β})-defected t-edge-coloring of G holds t≥ x'(λ_{1}, λ_{2}, …,λ_{β};G). We obtain Δ(G) ≤ x'(λ_{1}, λ_{2}, …,λ_{β};G) +(λ_{i}-1)≤ Δ(G) + 1, and introduce two new chromatic indices of G as: the vertex pan-biuniform chromatic index x_{pb}'(G), and the neighbour vertex pan-biuniform chromatic index x_{npb}'(G), and furthermore find the structure of a tree T having x_{pb}'(T) = 1.
Let n≥r, let π = (d_{1}, d_{2},…, d_{1}) be a non-increasing sequence of nonnegative integers and let K_{r+1}-e be the graph obtained from K_{r+1} by deleting one edge. If π has a realization G containing K_{r+1}-e as a subgraph, then π is said to be potentially K_{r+1}-e-graphic. In this paper, we give a characterization for a sequence π to be potentially K_{r+1}-e-graphic.
Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. We then present the definitions of the empirical likelihood-based Bayes information criteria (EBIC) and Akaike information criteria (EAIC). The results show that EBIC is consistent at selecting subset variables while EAIC is not. Simulation studies demonstrate that the proposed empirical likelihood confidence regions have better coverage probabilities than the least square method, while EBIC has a higher chance to select the true model than EAIC.
In this article, the empirical likelihood introduced by Owen Biometrika, 75, 237-249 (1988) is applied to test the variances of two populations under inequality constraints on the parameter space. One reason that we do the research is because many literatures in this area are limited to testing the mean of one population or means of more than one populations; the other but much more important reason is: even if two or more populations are considered, the parameter space is always without constraint. In reality, parameter space with some kind of constraints can be met everywhere. Nuisance parameter is unavoidable in this case and makes the estimators unstable. Therefore the analysis on it becomes rather complicated. We focus our work on the relatively complicated testing issue over two variances under inequality constraints, leaving the issue over two means to be its simple ratiocination. We prove that the limiting distribution of the empirical likelihood ratio test statistic is either a single chi-square distribution or the mixture of two equally weighted chi-square distributions.
An edge e of a k-connected graph G is said to be a removable edge if Ge is still k-connected, where Ge denotes the graph obtained from G by the following way: deleting e to get G-e, and for any end vertex of e with degree k-1 in G-e, say x, deleting x, and then adding edges between any pair of non-adjacent vertices in N_{G-e}(x). The existence of removable edges of k-connected graphs and some properties of k-connected graphs have been investigated. In the present paper, we investigate the distribution of removable edges on a spanning tree of a k-connected graph (k≥4).
Two constructions of cartesian authentication codes from unitary geometry are given in this paper. Their size parameters and their probabilities of successful impersonation attack and successful substitution attack are computed. They are optimal under some cases.
Let Γ= Cay(G, S), R(G) be the right regular representation of G. The graph Γ is called normal with respect toG, if R(G) is normal in the full automorphism group Aut(Γ) of Γ. Γ is called a bi-normal with respect toG, if R(G) is not normal in Aut(Γ), but R(G) contains a subgroup of index 2 which is normal in Aut(Γ). In this paper, we prove that connected tetravalent edge-transitive Cayley graphs on PGL(2, p) are either normal or bi-normal when p ≠11 is a prime.
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ||·||_{div,h} norm for p and optimal error estimates in L^{2} norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the one-dimensional quantum Navier-Stokes equations in a bounded domain is proved. The model consists of the mass conservation equation and a momentum balance equation, including a nonlinear third-order differential operator, with the quantum Bohm potential, and a density-dependent viscosity. It is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time, if the viscosity constant is not bigger than the scaled Planck constant. The proof is inspired by an observable constructed by Gamba, Gualdani and Zhang, which has been used to study the blowing up of solutions to quantum hydrodynamic models.
We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximal monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.
This paper is investigate the regularity criteria of weak solutions to the three-dimensional microp-olar fluid equations. Several sufficient conditions in terms of some partial derivatives of the velocity or the pressure are obtained.
We extend the Melnikov method to non-smooth dynamical systems to study the global behavior near a non-smooth homoclinic orbit under small time-periodic perturbations. The definition and an explicit expression for the extended Melnikov function are given and applied to determine the appearance of transversal homoclinic orbits and chaos. In addition to the standard integral part, the extended Melnikov function contains an extra term which reflects the change of the vector field at the discontinuity. An example is discussed to illustrate the results.