On absolute ruin minimization under a diffusion approximation model

In this paper, we assume that the surplus process of an insurance entity is represented by a pure diffusion. The company can invest its surplus into a Black-Scholes risky asset and a risk free asset. We impose investment restrictions that only a limited amount is allowed in the risky asset and that no short-selling is allowed. We further assume that when the surplus level becomes negative, the company can borrow to continue financing. The ultimate objective is to seek an optimal investment strategy that minimizes the probability of absolute ruin, i.e. the probability that the liminf of the surplus process is negative infinity. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is analyzed and a verification theorem is proved; applying the HJB method we obtain explicit expressions for the S-shaped minimal absolute ruin function and its associated optimal investment strategy. In the second part of the paper, we study the optimization problem with both investment and proportional reinsurance control. There the minimal absolute ruin function and the feedback optimal investment-reinsurance control are found explicitly as well.     

积分方程平面反射阵电磁建模技术

针对基于空间功率合成的空馈平面反射阵(FLAPS)型高功率微波辐射器的高效率电磁仿真需求,应用积分方程方法结合多尺度混合电磁建模技术MLFMA-MLACE进行问题的电磁建模及求解,主要过程包括：针对设计模型进行多尺度几何建模;在宏观层面采用多层快速多极子加速矩矢相乘;在微观层面采用多层笛卡尔展开加速求解。结合W波段的FLAPS初步模型,利用传统多层快速多极子技术（MLFMA）进行了精度验证,对于混合方法在仿真中的适用性、模型等效处理程度的影响以及计算成本等进行了分析。结果表明,该方法在内存及计算时间方面显著地提高了效率,论文还对后续改进方向进行了讨论。     

The Local Stark Conjecture at a Real Place

A refinement of the rank 1 Abelian Stark conjecture has been formulated by B.Gross. This conjecture predicts some IE1.gif" alt=" $$\mathfrak{p}$$ " align="middle" border="0"> -adic analytic nature of a modification of the Stark unit. The conjecture makes perfect sense even when IE2.gif" alt=" $$\mathfrak{p}$$ " align="middle" border="0"> is an Archimedean place. Here we consider the conjecture when IE3.gif" alt=" $$\mathfrak{p}$$ " align="middle" border="0"> is a real place, and interpret it in terms of 2-adic properties of special values of L-functions. We prove the conjecture for CM extensions; here the original Stark conjecture is uninteresting, but the refined conjecture is nontrivial. In more generality, we show that, under mild hypotheses, if the subgroup of the Galois group generated by complex conjugations has less than full rank, then the refined conjecture implies that the Stark unit should be a square. This phenomenon has been discovered by Dummit and Hayes in a particular type of situation. We show that it should hold in much greater generality.     

An Application of U(g)-bimodules to Representation Theory of Affine Lie Algebras

Let IE1.gif" alt=" $$\hat {\mathfrak{g}}$$ " align="middle" border="0"> be the affine Lie algebra associated to the simple finite-dimensional Lie algebra IE2.gif" alt=" $${\mathfrak{g}}$$ " align="middle" border="0"> . We consider the tensor product of the loop IE3.gif" alt=" $$\hat {\mathfrak{g}}$$ " align="middle" border="0"> -module IE4.gif" alt=" $$\overline {V\left( \mu \right)} $$ " align="middle" border="0"> associated to the irreducible finite-dimensional IE5.gif" alt=" $${\mathfrak{g}}$$ " align="middle" border="0"> -module V() and the irreducible highest weight IE6.gif" alt=" $$\hat {\mathfrak{g}}$$ " align="middle" border="0"> -module L _k,. Then L _k, can be viewed as an irreducible module for the vertex operator algebra M _k,0. Let A(L _k,) be the corresponding IE7.gif" alt=" $$A\left( {M_{k,0} } \right)\left( { = U\left( {\mathfrak{g}} \right)} \right)$$ " align="middle" border="0"> -bimodule. We prove that if the IE8.gif" alt=" $${U\left( {\mathfrak{g}} \right)}$$ " align="middle" border="0"> -module IE9.gif" alt=" $$A\left( {L_{k,0} } \right) \otimes _{U\left( \mathfrak{g} \right)} V\left( \mu \right)$$ " align="middle" border="0"> is zero, then the IE10.gif" alt=" $${\hat {\mathfrak{g}}}$$ " align="middle" border="0"> -module IE11.gif" alt=" $$\left( {L_{k,0} } \right) \otimes _{U\left( {\mathfrak{g}} \right)} V\left( \mu \right)$$ " align="middle" border="0"> is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras.     

Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem

In this paper, we present a new semi-analytical method for solving linear and nonlinear Fredholm integral and integro-differential equations of the second kind and the systems including them. The main idea in this method is applying the mean value theorem for integrals. Some examples are presented to show the ability of the model. The results confirm that the method is very effective and simple.     

Resonant Local Systems on Complements of Discriminantal Arrangements and Sl2Representations

We calculate the skew-symmetric cohomology of the complement of a discriminantal hyperplane arrangement with coefficients in local systems arising in the context of the representation theory of the Lie algebra IE1.gif" alt=" $$\mathfrak{s}\mathfrak{l}_2$$ " align="middle" border="0"> . For a discriminantal arrangement in ^k, the skew-symmetric cohomology is nontrivial in dimension k–1 precisely when the 'master function' which defines the local system on the complement has nonisolated criticalpoints. In symmetric coordinates, the critical set is a union of lines. Generically, the dimension of this nontrivial skew-symmetric cohomology group is equal to the number of critical lines.     

Fractional Spin Through Quantum Affine Algebras with Vanishing Central Charge

We study the fractional decomposition of the quantum enveloping affine algebras IE1.gif" alt=" $$U_Q (\hat A(n))$$ " align="middle" border="0"> and IE2.gif" alt=" $$U_Q \left( {\hat C\left( n \right)} \right)$$ " align="middle" border="0"> with vanishing central charge in the limit IE3.gif" alt=" $$Q \to q = e^{\frac{{2i\pi }}{k}} $$ " align="middle" border="0"> . This decomposition is based on the bosonic representation and can be related to fractional supersymmetry and k-fermionic spin. The quantum affine algebras and the classical ones are equivalent in the fermionic realization.     

Normality-Type Properties and Covariant Functors

Topological properties similar to normality are considered in subspaces of products and powers of topological spaces, of spaces of closed subsets, and of spaces having the form IE1.gif" alt=" $$\mathcal{F}$$ " align="middle" border="0"> (X), where IE2.gif" alt=" $$\mathcal{F}$$ " align="middle" border="0"> is a normal functor. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 2, pp. 57–98, 2003.     

\mathcal{Q}-Universal Quasivarieties of Graphs

It is proved that a quasivariety K of undirected graphs without loops is IE2.gif" alt=" $$\mathcal{Q}$$ " align="middle" border="0"> -universal if and only if K contains some non-bipartite graph.     

Stability of Hypersurfaces with Constant r-Mean Curvature

We deal with compact hypersurfaces immersed in space forms with constant IE2.gif" alt=" $$r$$ " align="middle" border="0"> -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.