Lattices associated with vector spaces over a finite field

AbstractLet V denote the n-dimensional row vector space over a finite field Fq, and fix a subspace W of dimension n-d. Let L(n,d)=P∪{V}, where P is the set of all the subspaces of V intersecting trivially with W. Partially ordered by ordinary or reverse inclusion, two families of finite atomic lattices are obtained. This article discusses their geometricity, and computes their characteristic polynomials

A Continuous-Time Version of a Delegated Asset Management Problem

This paper develops a continuous-time model to study the widely used investment mandates in the institutional asset management industry. In this paper, just like He and Xiong (2013), we suppose that the asset management industry has a two-layered incentive structure, and fund families charging investors fixed management fees while compensating individual fund managers based on fund performance. Different from He and Xiong (2013), we suppose that the fund family aims to select an optimal incentive strategy to maximize its terminal benefits, while the fund manager needs to select the optimal effort level and the optimal investment portfolio to maximize his terminal net discounted compensation in a continuous-time model. By using dynamic programming principle and stochastic differential game theory, the optimal strategies and value functions of both sides are derived. At last, numerical studies are provided to illustrate the effects of all the parameters on the optimal strategies. The result reveals that the optimal incentive mechanism will redistribute both the benefit of the fund families and the cost of the fund managers’ effort

Two error-correcting pooling designs from symplectic spaces over a finite field

AbstractIn this paper, we construct two classes of t×n,se-disjunct matrix with subspaces in a symplectic space Fq(2ν) and prove that the ratio efficiency t/n of two constructions are smaller than that of D’yachkov et al. (2005) [2]