Acta Mathematicae Applicatae Sinica, English Series最新文献

This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification. Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irreducibility. We impose weak conditions to obtain the strict periodic stationarity and the geometric ergodicity of the process, via the theory of positive linear operators on a cone: it is supposed that zero belongs to the support of the driving noise density which is absolutely continuous with respect to the Lebesgue measure and the spectral radius of a matrix built from the periodic coefficients of the model is smaller than one.

In this paper, we propose a pricing model of airbag options with discrete monitoring, time-varying barriers, early exercise opportunities, and other popular features simultaneously. We show that the option value is a viscosity solution of a PDE system. In particular, a closed-form solution is obtained in the classic Black-Scholes economy with no early exercise opportunities. For the general case, we develop a numerical algorithm and conduct an extensive numerical analysis after calibrating the model to the CSI 500 index in China. Greek letters, dynamic hedging, and assessment of investing in airbag options are also studied.

Let Γ denote a bipartite Q-polynomial distance-regular graph with vertex set X, valency k ≥ 3 and diameter D ≥ 3. Let A be the adjacency matrix of Γ and let A*:= A*(x) be the dual adjacency matrix of Γ with respect to a fixed vertex x ∈ X. Let T:= T(x) denote the Terwilliger algebra of Γ generated by A and A*. In this paper, we first describe the relations between A and A*. Then we determine the dimensions of both T and the center of T, and moreover we give a basis of T.

This paper is devoted to the following fractional relativistic Schrödinger equation:

where (−Δ + m²)^s is the fractional relativistic Schrödinger operator, s ∈ (0, 1), m > 0, V: ℝ^N → ℝ is a continuous potential and f: ℝ^N × ℝ → ℝ is a superlinear continuous nonlinearity with subcritical growth. We consider the case where the potential V is indefinite so that the relativistic Schrödinger operator (−Δ + m²)^s + V possesses a finite-dimensional negative space. With the help of extension method and Morse theory, the existence of a nontrivial solution for the above problem is obtained.

The purpose of this work is to investigate the boundedness of the pullback attractors for the micropolar fluid flows in two-dimensional unbounded domains. Exactly, the H¹-boundedness and H²-boundedness of the pullback attractors are established when the external force F(t, x) has different regularity with respect to time variable, respectively.

In this paper, we study the problem of irreversible investment under endowment constraints. We first establish the existence and uniqueness of the result and then demonstrate the necessity and sufficient conditions for optimality. Based on this condition, we provide a characterization for optimal investment plans, which can be obtained by the so-called base capacity solving a backward equation. We may obtain explicit solutions for certain typical cases.

In this paper, we consider the Cauchy problem of the d-dimensional damping incompressible magnetohydrodynamics system without dissipation. Precisely, this system includes a velocity damped term and a magnetic damped term. We establish the existence and uniqueness of global solutions to this damped system in the critical Besov spaces by means of the Fourier frequency localization and Bony paraproduct decomposition.

In this article, we study the empirical likelihood (EL) method for autoregressive models with spatial errors. The EL ratio statistics are constructed for the parameters of the models. It is shown that the limiting distributions of the EL ratio statistics are chi-square distributions, which are used to construct confidence intervals for the parameters of the models. A simulation study is conducted to compare the performances of the EL based and the normal approximation (NA) based confidence intervals. Simulation results show that the confidence intervals based on EL are superior to the NA based confidence intervals.

In this paper, we propose an efficient and accurate method for pricing Guaranteed Minimum Death Benefit (GMDB) under time-changed Lévy processes. Suppose that the GMDB payoff depends on a dollar cost averaging (DCA) style periodic investment, and the activity rate process in stochastic time change is modeled by a square-root process. We develop a recursive method to derive the closed form valuation formula by using the frame duality projection method. Numerical examples are reported for demonstrating the effectiveness of our approach and illustrating the interplay between contract parameters and the valuation.

In this paper, ({overline partial})-dressing method based on a local 3 × 3 matrix ({overline partial})-problem with non-normalization boundary conditions is used to investigate coupled two-component Kundu-Eckhaus equations. Firstly, we propose a new compatible system with singular dispersion relation, that is time spectral problem and spatial spectral problem of coupled two-component Kundu-Eckhaus equations via constraint equations. Then, we derive a hierarchy of nonlinear evolution equations by introducing a recursive operator. At last, by solving constraint matrixes, a spectral transform matrix is given which is sufficiently important for finding soliton solutions of potential function, and we obtain N-soliton solutions of coupled two-component Kundu-Eckhaus equations.