常数相对风险厌恶多单位拍卖的比较静态与定价结构

传统的H∞鲁棒控制器通常都是基于线性矩阵不等式求解的,因此阶次较高,不利于实现,而基于Nevanlinna-Pick插值的H∞鲁棒控制器设计方法能够有效的解决这一问题。本文提出一种改进的同伦算法用于求解控制器设计过程中出现的非线性方程,避免了经典同伦法中逆矩阵的求解。针对某一跟踪系统设计基于Nevanlinna-Pick插值的H∞鲁棒控制器,通过阶跃响应和正弦信号的跟踪响应可以看出,与高阶超前滞后校正环节相比,前者构成闭环系统的跟踪精度要比后者的控制精度高,且具有较强的鲁棒稳定性。

The Comparative Static and Pricing Structure of Multi-Unit Discriminatory Auctions with Constant Relative Risk-aversion Bidders

This paper considered multi-unit discriminatory auctions with constant relative risk-aversion bidders, and explored the special structure of its equilibrium strategy and how the risk preferences of the bidders, also the distributions of bidders'' value influenced the equilibrium bids. By introducing the concept of risk-neutral equivalent distribution, the case of constant relative risk-aversion was transformed into the case of risk-neutral. This transformation enables us to combine the influences of the risk preferences and distributions upon the bids to get an equivalent condition for the comparative relation. The situations in which different bidders have different constant relative risk-aversions shows that the equilibrium bids depend linearly on risk reference parameters. Based on this pricing structure, this paper introduced the concepts of "demanded surplus", "competition surplus" and "risk-aversion surplus", and finds that the first one can be decomposed to be the algebraic sum of the latter two.