A Bowley solution with limited ceded risk for a monopolistic reinsurer

Borch (1969) advocated that the study of optimal reinsurance design should take into consideration the conflicting interests of both an insurer and a reinsurer. Motivated by this and exploiting a Bowley solution (or Stackelberg equilibrium game), this paper proposes a two-step model that tackles an optimal risk transfer problem between the insurer and the reinsurer. From the insurer’s perspective, the first step of the model provisionally derives an optimal reinsurance policy for a given reinsurance premium while reflecting the reinsurer’s risk appetite. The reinsurer’s risk appetite is controlled by imposing upper limits on the first two moments of the coverage. Through a comparative analysis, the effect of the insurer’s initial wealth on the demand for reinsurance is then examined, when the insurer’s risk aversion and prudence are taken into account. Based on the insurer’s provisional strategy, the second step of the model determines the monopoly premium that maximizes the reinsurer’s expected profit while still satisfying the insurer’s incentive condition. Numerical examples are provided to illustrate our Bowley solution.     

Nonlocal stochastic differential equations with time-varying delay driven by G-Brownian motion

This article studies a class of nonlocal stochastic differential equations driven by G-Brownian motion (G-NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G-Lyapunov functional and ψ-type function.     

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

Comparative structural analysis of a histone-like protein from Spiroplasma melliferum in the crystalline state and in solution

A solution of a histone-like protein from Spiroplasma melliferum (HUSpm) was examined by small-angle X-ray scattering (SAXS). The experimental SAXS curve was compared with those calculated for the HUSpm structures from the PDB databank obtained by both X-ray diffraction analysis and nuclear magnetic resonance spectroscopy. The model of the HUSpm structure in solution, which best agrees with the experimental SAXS data, has a shorter distance between the centers of mass of the HUSpm monomers compared to the crystal structure, indicating that the HUSpm monomers can be located closer to each other in solution than in the crystalline state.     

Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论，研究了Boussinesq方程，通过对Boussinesq方程进行行波变换，得到了相应行波系统的首次积分和平衡点，给出了不同参数条件下的相图，证实了Boussinesq方程存在孤立波解和周期波解。     

一致分数阶非线性微分方程的精确解

同时考虑了Kudryashov方法和Khalil一致分数阶变换,构造了求解一致分数阶非线性微分方程精确解的新方法,并将其用于求解时间-空间一致分数阶Whitham-Boroer-Kaup方程,得到了Whitham-Boroer-Kaup方程新的精确解,验证了该方法的有效性和可行性.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.