FlexAuc: Serving Dynamic Demands in a Spectrum Trading Market with Flexible Auction

In secondary spectrum trading markets, auctions are widely used by spectrum holders (SHs) to redistribute their unused channels to secondary wireless service providers (WSPs). As sellers, the SHs design proper auction schemes to stimulate more participants and maximize the revenue from the auction. As buyers, the WSPs determine the bidding strategies in the auction to better serve their end users. In this paper, we consider a three-layered spectrum trading market consisting of the SH, the WSPs and the end users. We jointly study the strategies of the three parties. The SH determines the auction scheme and spectrum supplies to optimize its revenue. The WSPs have flexible bidding strategies in terms of both demands and valuations considering the strategies of the end users. We design FlexAuc, a novel auction mechanism for this market to enable dynamic supplies and demands in the auction. We prove theoretically that FlexAuc not only maximizes the social welfare but also preserves other nice properties such as truthfulness and computational tractability.Comment: 11 pages, 7 figures, Preliminary version accepted in INFOCOM 201

Weighted estimation of the dependence function for an extreme-value distribution

Bivariate extreme-value distributions have been used in modeling extremes in environmental sciences and risk management. An important issue is estimating the dependence function, such as the Pickands dependence function. Some estimators for the Pickands dependence function have been studied by assuming that the marginals are known. Recently, Genest and Segers [Ann. Statist. 37 (2009) 2990-3022] derived the asymptotic distributions of those proposed estimators with marginal distributions replaced by the empirical distributions. In this article, we propose a class of weighted estimators including those of Genest and Segers (2009) as special cases. We propose a jackknife empirical likelihood method for constructing confidence intervals for the Pickands dependence function, which avoids estimating the complicated asymptotic variance. A simulation study demonstrates the effectiveness of our proposed jackknife empirical likelihood method.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ409 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained

Local time and Tanaka formula for G-Brownian Motion

In this paper, we study the notion of local time and Tanaka formula for the G-Brownian motion. Moreover, the joint continuity of the local time of the G-Brownian motion is obtained and its quadratic variation is proven. As an application, we generalize It^o's formula with respect to the G-Brownian motion to convex functions.Comment: 29 pages, "Finance and Insurance-Stochastic Analysis and Practical Methods", Jena, March 06,200