基于新巴塞尔协议监管下保险人的均值-方差最优投资-再保险问题

本文研究了均值-方差优化准则下,保险人的最优投资和最优再保险问题.我们用一个复合泊松过程模型来拟合保险人的风险过程,保险人可以投资无风险资产和价格服从跳跃-扩散过程的风险资产.此外保险人还可以购买新的业务(如再保险).本文的限制条件为投资和再保险策略均非负,即不允许卖空风险资产,且再保险的比例系数非负.除此之外,本文还引入了新巴塞尔协议对风险资产进行监管,使用随机二次线性(linear-quadratic,LQ)控制理论推导出最优值和最优策略.对应的哈密顿-雅克比-贝尔曼(Hamilton-Jacobi-Bellman,HJB)方程不再有古典解.在粘性解的框架下,我们给出了新的验证定理,并得到有效策略(最优投资策略和最优再保险策略)的显式解和有效前沿.     

Nonlinear Double-well Schrödinger Equations in the Semiclassical Limit

We consider time-dependent Schrödinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of the beating period and the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimension d=1 or d=2.     

Critical point approaches to Gradient-Type systems on the Sierpi\'{n}ski Gasket

We investigate the existence of multiple solutions for parametric quasi-linear systems of the gradient-type on the Sierpi\''{n}ski gasket. We give some new criteria to guarantee that the systems have at least three weak solutions by using a variational method and some critical points theorems due to Ricceri. We extend and improve some recent results. Finally, we give two examples to illustrate the main results.     

The existence of global solutions for the fourth-order nonlinear Schrodinger equations

In this paper, the problem of a class of multidimensional fourth-order nonlinear Schr\"{o}dinger equation including the derivatives of the unknown function in the nonlinear term is studied, and the existence of global weak solutions of nonlinear Schr\"{o}dinger equation is proved by the Galerkin method according to the different values of $\lambda$.     

Optimal investment strategies and risk-sharing arrangements for a hybrid pension plan

A continuous time stochastic model is used to study a hybrid pension plan, where both the contribution and benefit levels are adjusted depending on the performance of the plan, with risk sharing between different generations. The pension fund is invested in a risk-free asset and multiple risky assets. The objective is to seek an optimal investment strategy and optimal risk-sharing arrangements for plan trustees and participants so that this proposed hybrid pension system provides adequate and stable income to retirees while adjusting contributions effectively, as well as keeping its sustainability in the long run. These goals are achieved by minimizing the expected discount disutility of intermediate adjustment for both benefits and contributions and that of terminal wealth in finite time horizon. Using the stochastic optimal control approach, closed-form solutions are derived under quadratic loss function and exponential loss function. Numerical analysis is presented to illustrate the sensitivity of the optimal strategies to parameters of the financial market and how the optimal benefit changes with respect to different risk aversions. Through numerical analysis, we find that the optimal strategies do adjust the contributions and retirement benefits according to fund performance and model objectives so the intergenerational risk sharing seem effectively achieved for this collective hybrid pension plan.     

非线性离散微分方程的双曲函数法求解

本文推广了双曲函数方法用于求解非线性离散系统。求解离散的(2+1)维Toda系统和离散的mKdV系统，成功地得到了离散钟型孤立子、离散冲击波型孤立子及一些新的精确行波解。     

Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises

It is shown how the cross-correlation time and strength of coloured cross-correlated white noises can set an upper bound for the time derivative of entropy in a nonequilibrium system. The value of upper bound can be calculated directly based on the Schwartz inequality principle and the Fokker--Planck equation of the dynamical system driven by coloured cross-correlated white noises. The present calculations can be used to interpret the interplay of the dissipative constant and cross-correlation time and strength of coloured cross-correlated white noises on the upper bound.     

Equivalence Relation between Initial Values and Solutions for Evolution p-Laplacian Equation in Unbounded Space

In this paper,an equivalence relation between the ω-limit set of initial values and the ω-limit set of solutions is established for the Cauchy problem of evolution p-Laplacian equation in the unbounded space Yσ(RN).To overcome the difficulties caused by the nonlinearity of the equation and the unbounded solutions,we establish the propagation estimate and the growth estimate for the solutions.It will be demonstrated that the equivalence relation can be used to study the asymptotic behavior of solutions.     

平板几何迁移算子的特征值问题

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